The video covers the four steps which are,
Set up two cases
Rewrite without the absolute valur bar
Solve the inequality
Place on a number line
Friday, November 8, 2013
Absolute Value Inequalities
The video covers the four steps which are,
Set up two cases
Rewrite without the absolute valur bar
Solve the inequality
Place on a number line
Monday, September 2, 2013
Prime Factorization
Video of the Day
Prime factorization is when you take any number and determine which prime numbers when multiplied together equal this number.
In this video you will learn…..
A definition of prime factorization
How to set up a factor tree
A easy method of prime factorization
Watch an example problem of prime factorization with step by step directions
Definition of a composite and prime numbers
For more information,a prime factorization calculator, and a prime number chart see
Wednesday, August 28, 2013
Area of a Rhombus
Video of the day
Today we are going to look at finding the area of a Rhombus
In this video you will ……..
Learn two methods for finding the area of a Rhombus
Watch two sample problems.
Learn the difference between altitude and height.
Learn why you can’t square the sides for the area but need to use the altitude.
How to find the area of a rhombus when the altitude is unknown
How to calculate the area by using the diagonals of a rhombus.
For more information please see Area of a Rhombus or Area Formulas Plane Shapes
Tuesday, August 27, 2013
Prime Factorization
Featured Video of the Day
Prime factorization is the process of finding which prime numbers when multiplied together equal the original number. In this video you will learn…
A simple, but very effective method of prime factorization.
A step by step example of prime factorization
The definition of Prime Factorization
The definition of prime numbers
For more information and a prime factorization calculator please see
Monday, August 26, 2013
Finding Area of Triangle on a Coordinate Plane
Featured Video of the Day
Finding the area of a Triangle on a coordinate plane.
Imagine you have to drive to watch your favorite sports team play. Based on many factors like traffic, time, or road conditions, there are many different paths you could follow to arrive at your destination. In the same fashion, there are several paths one can take to calculate the area of a triangle based on the information given. The video of the day describes one method.
In this video you will learn.......
A method that can be used to find the area of a triangle when altitude is not given.
A method to find the area of a triangle without a right angle.
How to use the three vertices to find the area of a triangle.
The formula for finding the area using the coordinate plane method.
Watch an example problem using the coordinate plane method.
For more information please see Area of a triangle
Sunday, August 25, 2013
Complementary Angles
Featured video of the day
Hope this video helps out in Math class.
In this video you will learn.
Definition of Complementary Angles
How to determine if an angle is complementary or a supplementary angle.
A sample problem involving complementary angles
Definition of a supplementary angle
For more information please see Complementary Angles
Tuesday, August 20, 2013
Area of a triangle
The goal of this post is to give you several methods for finding the area of a triangle and a video that goes with each method. The method used to find the area is based on the information you are given.
If you know the Base and Altitude use half base times height
If you don’t know the altitude use Heron’s formula
If you know Two sides and included angle use Side Angle Side ( SAS)
If you know X and Y vertices of the corners use Box Method
If you know Triangle is equilateral use Equilateral Triangle Area
If you know Triangle is isosceles use ½ base times height
Video Half base * height
For even more information on finding the area of a triangle please see.Finding the area of a triangle
Sunday, August 11, 2013
Finding the area of a triangle
The goal of this post is to give you several methods for finding the area of a triangle and a video that goes with each method. The method used to find the area is based on the information you are given.
If you know the Base and Altitude use half base times height
If you don’t know the altitude use Heron’s formula
If you know Two sides and included angle use Side Angle Side ( SAS)
If you know X and Y vertices of the corners use Box Method
If you know Triangle is equilateral use Equilateral Triangle Area
If you know Triangle is isosceles use ½ base times height
Video Half base * height
For even more information on finding the area of a triangle please see.Finding the area of a triangle
Sunday, August 4, 2013
Area of Plane Figures
Finding area of plane figures
Area is the space covered in a flat, 2-dimensional plane inside a bounded region. Think of area in terms of painting a wall. The area of plane shapes is the amount of units squared that can fit inside the shape. It is measured in units squared.
When finding the area of plane figures you need specific measures. One of the greatest lessons for students is deciding what information they have given and which formula they need to use to find the area of the plane figures.
Area can also be found on a coordinate plane using order pairs to find necessary dimensions.
You can access videos and informational pages for each of the plane shapes on our area of plane figures formula page. The following plane figures are covered.
Triangles
Circle
Trapezoid
Parallelogram
Rectangle
Square
Rhombus
Also, for most of the plane figures I have a calculator that calculates area, diagonal length, and volume for each of the plane figures. Here is a link to Math calculators
Tuesday, July 30, 2013
Plane shapes
Plane Shapes
What is a plane shape? A plane shape is a closed, two-dimensional shape. Plane shapes vary according to the numbers of sides or vertices. A vertex is where two sides meet. If a draw a line from two vertices that are not next to each other this line would be called a diagonal.
There are many plane shapes and here is a list of several common plane shapes.
A triangle is a plane shape with three sides and three vertices. Here is a list of some common triangles.
Scalene triangles have three different side lengths and three different angle measures
Isosceles triangles have at least two equal sides and two equal angle measures
Equilateral triangles have equal sides and angles.
A rectangle is a shape with four sides and four vertices
A square is a rectangle in which all four sides are of equal length and create four ninety degree angles.
A circle is a round shape that has no sides or corners.
A parallelogram has four sides, four vertices, and two parallel sides.
A quadrilateral is a plane shape with four sides, four vertices, and two diagonals. There are many types of quadrilaterals and check here for a chart of the quadrilateral family.
A rhombus has four sides, four vertices, and four equal sides.
A trapezoid has four sides, four vertices, and exactly one pair of parallel sides.
Polygons are plane shapes classified by the number of sides. The number of sides and vertices are equal in polygons.
Classifying polygons by the number of sides
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 septagon
8 octagon
9 nonagon
10 decagon
12 dodecagon
n n-gon
Saturday, July 20, 2013
Common Triples
In this video you will....
Look at common triples associated with the pythagoren theorem
How to use common triples to find a missing leg of a right triangle
Examples of common triples that are frequently seen in Geometry
Hi welcome to MooMooMath. Today we are going to look at common triples which are associated with the Pythagorean Theorem. Here is a common triple., a three, four, five which works in the Pythagorean theorem because 3 squared ( 9 ) plus four squared ( 16 ) equals 5 squared ( 25 16 + 9 equals 25 ) so we have the numbers three. Four and five which are a common triple. In the Pythagorean Theorem. Below it is a triangle with a side of 6 and a hypotenuse of 10 and an X as the unknown side of X if you will notice this shows you a common triple. So three and 6 are associated with each other so they are corresponding sides and if I double 3 I get 6 and if I double 5 I get 10. Therefore if I double 4 I get 8 so the missing side is 8 so this is just applying the Pythagorean Theorem triple to an actual problem. So what are the actual rules for doing this? So what you will do is take your common triplets and multiple each number by the same factor. So we have a three, four, and five and in the example we multiplied each side by two to get a six, eight, ten triangle. You can also go back and multiple 3, 4, 5 by three and get 9, 12. and 15. You get do that with 4 10 or a 40, 50 right triangle. So what are the common triples? Let me show you several of the common triples you will see. 3, 4, 5 and multiples of those. A 5, 12, 13 is also a common triple. Because 5 squared plus 12 squared equals 13 squared. 25 plus 144 equals 169. Here are three more common triples 7, 24, 25 the 8, 15, 17 and the 20, 21, 29. So those are common triples you can take and multiple by sides by common factors. So you can see how this is done. Since I showed you the 3, 4, 5 triple first this time I will use the 5, 12, and 13. So if I were to make a table of possible values I will just draw the 5, 12, and 13 on top and make a list. If I multiple by two I get 10, 24, and 26. And multiple by three I get 15 26, 39 and by 4 I get 20 48 and 52 and those would be our common triples of 5, 12, 13. Hope this was helpful
Math Resource Page
Check out our new math resource page. I designed the resource page to be helpful for teachers and students. I currently teach Math at a public high school, and tried to think through what would help the teachers I work with, and the students I teach. Next, went blog stalking and checked out all the blogs of good teachers I know and tried to find out resources that they had attached to their blog. Here is a list of resources I hope will help you in your Math class.
First, I have a long list of applets. Applets are a graphical approach to math concepts. They are good for demonstrating algebraic, geometry, and calculus concepts. I tested each applet and made sure they worked.
Graph paper
I included five or six links to free graph paper. Some sites you can design the graph paper you want.
Calculators
I have several links to different types of online calculators. Some of the calculators are basic, other are scientific or graphing calculators.
Calculator Shortcuts and Instruction
I have a long list of short cuts, manuals, and instructions for the TI83, TI84, and the TI89. I tried to find sites that had pictures and illustrations
Classroom Help
These resources include many links that will help the student and teacher with projects, presentations, and other creative ways to present material. I work with a great and award winning media specialist and these are sites she recommends.
Math Sites
I found several sites that just have an amazing number of math links and resources. In fact one site has over 1000 links to work sheets, and lessons on math concepts.
Math Gift Shop
I have links to Math T-shirts, coffee mugs and other math related items that every math teacher or student would love to have. Even if you hate math you can always get your favorite math teacher a gift.
Please check out our Math Resource page here. Thanks and if you like it please share it with your friends.
Friday, June 28, 2013
Special rules for 30-60-90 Triangle
Video Special Rules 30-60-90 Triangle
In this video you will learn...
- How to identify the short leg,long leg, and the hypothesis
- How to calculate the short leg given the long leg and hypothesis
- How to find the length of tegth of the long leg given the short leg in a 30-60-90 Triangle
- How to find the hypothenuse given the short leg
- Given the long leg of a 30-60-90 triangle how to find the two other legs
Transcript of the video
30=60=90 Triangles
Hi Welcome to MooMooMath. Today we are going to talk about 30-60-90 Triangles. Now there are a set of rules so let me go ahead and share these rules with you, and then we will look at the three different directions that you can use to solve these. The rules for 30-60-90 triangles are as follows. The short leg is always opposite the 30 degree angle. We will call the short leg S. The longer leg is always opposite the 60 degree angle. To find its length takes the short side times the square root of three. Our hypotenuse is always opposite the right angle. To find the hypotenuse take the short leg and multiple it by two. So our short leg is our starting point. Short leg is S Long leg is S times square root of three and hypotenuse is 2 times the short side. Or double the short leg. Let’s go back and work one of these. If we have the short leg all the rules are set. I double it to get the hypotenuse. So I take 2 times 3 so my hypotenuse is 6. Now to get the longer leg I take the short leg times the square root of 3. So I take 3 times the square root of 3 on a calculator or you can leave it as a rational answer. Let’s look at the second method. If given the hypotenuse and you have to figure out the other two sides. The easiest one to get is always the short leg because it is half the hypotenuse. You have a one to two ratio. So if my hypotenuse is 10 then half of that is 5. Once you get the short leg you can get the longer leg, which is the short leg times the square root of three. So it is just five square root three. Now let’s do the hardest direction. When you have the long leg and you’re trying to find the other two sides this is the most difficult direction because you are using the square root of three. Now to go from the short side to long side you multiple by the square root of three. So to go from the long to the short you would divide by the square root of three. So I am taking six divided by the square root of three to get the short leg. To rationalize that multiple the bottom by root three and the top by root three. Square root of three times the square root of three is three. So I have 6 square three over three and the coefficients divide so I have two square root three. Now that is your short leg. You always get the short leg first. So you double that to get the hypotenuse so two times two is four and the radical stays the same so your hypotenuse is four square root three. So those are your three directions. Hope this was helpful
Wednesday, June 26, 2013
How to find the surface area of a prism
How to find the surface area of a prism
First, what is a prism? A prism is a rectangular solid with a length, a width, and a height.
To find the surface area you are trying to figure out the total area of the surface of the prism.
The formula for finding the surface area equals
2* (length *width) + 2(length*height) + 2*(height * width) = Surface area of a prism
Find the surface area of a prism with a length of 6 units, a height of3 units and a width of 4 units.
Step 1. Plug in the appropriate units in the formula
2* (6*4) + 2(6*3) + 2( 3*4)
(L*W) ( L*H) (H*W)
Step 2. 2*24 + 2*18 + 2*12
Step 3. 48+36+24 = 108 units squared
Surface area is always squared
Thursday, June 20, 2013
How to find the volume of a sphere.
How to find the volume of a sphere
What is a sphere? You can think of a sphere as a circle in three dimensions. A sphere is perfectly symmetrical, does not have any vertices or corners, no edges. In addition, all of the points on a sphere are the same distance from the center.
The formula for finding the volume of a sphere equals 4⁄3 Ï€r^3 r =radius
Step 1. Plug 6 in the formula for the radius
Step 2. 4⁄3 Ï€6^3 = 4⁄3 Ï€216
Step 3. Multiply 4⁄3 x 216=( 4*216 )/3
Step 4 864/3 = 288Ï€ units^3
Saturday, June 15, 2013
Volume of a Rectangular Prism
How to find the volume of a rectangular prism ?
Video Volume Rectangular Prism
How do you find the volume of a rectangular prism? A rectangular prism is a three dimensional shape with two rectangular parallel bases. The formula for finding the volume of a rectangular prism is base area times the height. ( Ba * h )
Problem 1. Find the volume of a rectangular prism that has a base of 4 units and 7 units, and a height of 5 units.
Step 1. Use the formula for finding volume which equals V= Ba * h
H = height
Step 2. Find the base area of a rectangle Ba = Length x Width
4* 7 = 28 units
Step 3. Multiply the Ba * height
28 * 7 = 140 units cubed
Thursday, June 13, 2013
Finding the Perimeter of an Equilateral Triangle
Finding the perimeter of an equilateral triangle
First, an equilateral triangle is a triangle that has three equal sides. In order to find the perimeter you can add the three sides together or you can just three times the length of one side.
Video Perimeter of an Equilateral Triangle
Problem 1. Find the perimeter of an equilateral triangle with a side of twelve units.
Step 1. 3*12 = 36 units
Problem 2. Find the perimeter of an equilateral triangle with an altitude of 12 units.
Step 1. Find the length of one side. The altitude creates a 30-60-90 triangle. The altitude becomes the long side of a 30-60-90 triangle.
Step 2. In order to get the side length use (long side of 30-60-90 triangle)/√3 which equals 12/√3
For a review of 30-60-90 rules check here
Step 3. 12/√3 = 4√3 which is the length of half of the equilateral side length
Step 4. In order to get the entire length take 2* 4√3 =
Step 5. Now you can use 3 * the side length or 3* 8√3= 24√(3 ) units
Wednesday, June 12, 2013
Volume of a pyramid
What is a pyramid? A pyramid is a three dimensional figure that has a base and an apex which you can think of as a point.
The formula for volume equals 1/3 * base * height
The base area will depend on the shape of the base.
For example if the shape of the base is a square you would just multiple length times width
If the shape is a triangle you would take ½ base * height to get the base and then multiply this by the height of the triangle.
Check here for a list of base area formulas.
Problem 1. Find the volume of a pyramid with a square base that has a side of 4 units and a height of 5 units.
Step 1. Find the base area 4 * 4 = 16 units
Step 2. Multiply base area times height = 16* 5 = 80 units
Step 3. Multiply this by 1/3 ( remember the formula is 1/3 * base * height = 1/3*80 = 26.6 units cubed
Problem 2. Find the volume of a pyramid with a triangle base with a base of 6 units and a height base of 8 units and a pyramid height of 7 units
Step 1. Find the base area using the formula ½ base * height
Step 2. ½ * 6 * 8 = 24 units
Step 3. Find the volume using 1/3 * base * height3
Step 4. 1/3 * 24 * 7 = 8*7
Step 5. 8*7 = 56 units cubed
How to find the volume of a prism
Here is the problem worked on video
What is a prism? A prism is a three dimensional figure with parallel bases.
The formula for finding the volume of a prism is just length X width X height
Let’s look at a problem
What is the volume of a prism with a base of 6 by 7 units and a height of 9 units?
Step 1 Plug the units into the formula l * w * h 6*7*9
Step 2. Multiply 6*7*9 = 42*9
42*9 = 378 units cubed (volume is always cubed)
Now a prism can be have different shaped bases. The key to finding the volume is to find the base area formula for that shape and then multiply this by the height.
Check here for a list of most base area formulas
For example, if you had a triangle shaped prism you would use ½ base x length x height to find the volume of the triangular prism
Tuesday, June 11, 2013
Finding the volume of a Cone given the slant height
Finding the Volume of a Cone given the Slant Height
Here is the video that works the volume of a cone using the slant height
Problem 1 Find the volume of a cone with a slant height of 9 units and a diameter of 12 units.
Step 1 Find the radius by taking ½ of the diameter
½ * 12 =6 units
Step 2 Notice that the slant height is part of a right triangle. We need the height to figure out the volume. The formula for volume = πr^2*h
Step 3. We can use the Pythagorean Theorem to find the height.
The radius becomes the leg of the right triangle
The slant height becomes the hypotenuse of the right triangle
So for the height I will use a^2+ 6^2= 9^2
Step 3a a^2+ 36= 81
Step 3b a^2= 45
Step 3c a= √(45 ) this simplifies to 3√5
Step 4 So now use the volume formula πr^2*h
Step 4a Ï€6^2*3√5
Step 4b 36Ï€* 3√5
Step 4c 108√5 Ï€ units^3 is the volume
Sunday, June 9, 2013
Finding the volume of a cone
The formula for the volume of a cone = 1⁄3 Ï€r^2*h
h =height
r = radius
Please note πr^2*h is actually the volume of a cylinder that has the same height and radius. However it takes three cones to fill up a cylinder so that is why you multiply by 1/3
Problem 1. Find the volume of a cone with a height of 10 and a radius of 6 units.
Click the cone above for additional information
Step 1. Plug your numbers into the formula.
1⁄3 Ï€6^2*10
Step 2 Simplify 1⁄3 Ï€6^2*10
Step 2b 1⁄3 Ï€36*10
Step 3 1⁄3 x 36⁄1 Ï€ x 10
Step 3b 12Ï€ x 10=120Ï€ units^3 (Please note volume is always cubed)
Thursday, June 6, 2013
Volume of a Cube
Finding the Volume of a Cube
The formula for the volume of a cube equals one side raised to the third power.
Volume = s^3
Problem 1 What is the volume of a cube with a side length of 3 units?
Step 1 3*3*3 or 3^3 = 27 units ^3
Problem 2 This problem is slightly more challenging.
Find the volume of a cube with a diagonal length of 6 units.
Step 1. Use your 45-45-90 rules of a triangle to find the length of one side.
Step 2. The diagonal cuts the side of the cube into two 45 degree angles. See below.
Step 3. The side length will equal Hypotenuse √2 = 6√2
Step 4 Rationalize. 6/√2 * √2/√2 = (6√2)/2 =3√2 = one side
Step 5 Now I just need to cube the side (3√2 )^3 = 3*3*3 *√2*√2*√2
3*3*3 *√2*√2*√2 = 27*2√2
27*2√2 = 54√(2 ) units^3
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Wednesday, June 5, 2013
Volume of a Cylinder
Finding the volume of a cylinder
The formula for finding the volume of a cylinder equals πr^(2 )* h
The πr^(2 ) equals the area of the base and the h equals the height of the cylinder
Problem 1 Find the volume of the cylinder that has a diameter of 6 units
and a height of 8 units.
Step 1 Find the radius by dividing the diameter in half.
6 /2 = 3 units which is r or the radius
Step 2. Plug the radius into πr^(2 ) which equals π3^(2 )
9Ï€ = base area of the cylinder
Step 3. 9Ï€ * height which equals 9Ï€ * 8 = 72Ï€ units^3 (remember that
volume is always units cubed)
Monday, June 3, 2013
How to find the Area of a Parallelogram
How to find the Area of a Parallelogram
Video How to find the Area of a Parallelogram
The formula for finding the area of a parallelogram equals base times height or A=b*h
Please note, the height is not the length of a side but is the distance from base to base. Please see the drawing below.
Problem 1. What is the area of a parallelogram with a base of 8 units and sides of 5 units and a height of 4 units?
Step 1. Multiply the base of 8 units times the height of 4 units.
Step 2. 8*4 = 32 units squared
Problem 2. What is the area of a parallelogram that has a side of 6 units, a base of 10 units and an angle measure of 60 degrees?
Step 1. Find the altitude. If you draw a vertex straight down it creates a triangle. See picture below. The triangle is a 30-60-90 triangle. I can use the 30-60-90 rules to find the height of the parallelogram.
The rules of a 30-60-90 are as follows:
Short leg =x
Long leg = x√3
Hypotenuse = 2x
Step 2. The length of the side leg equals 6 and is my hypotenuse in my triangle
Therefore, 6 =2x so x =3
Step 3. Now that I know x I can find the height by finding the length of the long leg
long leg=3√3
Step 4. Use area equals base * height or A =b*h
10 * 3√3 = 30√3 units^2
Saturday, June 1, 2013
Top Ten Properties of a Parallelogram
Top Ten Properties of a Parallelogram
1. A parallelogram is a quadrilateral.
2. The opposite sides of a parallelogram are parallel.
3. The opposite angles of a parallelogram are congruent.
4. The opposite sides of a parallelogram are congruent.
5. The perimeter of a parallelogram equals 2 (base + side)
6. The area of a parallelogram equals base * height
7. The adjacent angles of a parallelogram are supplemental.
8. The diagonals of a parallelogram bisect each other. (In other words the cut each other exactly in half.
9. A parallelogram has four sides
10. The sides of a parallelogram must be straight.
Top Ten Properties of a Rhombus
Top Ten Properties of a Rhombus
1. A rhombus falls in the quadrilateral family so it has four sides.
2. A rhombus is also a parallelogram and has the properties of a parallelogram
3. A rhombus has congruent opposite sides that are parallel
4. All four sides of a rhombus are congruent
5. Opposite angles in a rhombus are congruent.
6. The diagonals of a rhombus are perpendicular.
7. The diagonals cross and make four right angles.
8. The perimeter of a rhombus equals 4 x one side
9. The area of a rhombus equals ½(Diagonal 1* Diagonal 2) or Base * Height (not the length of the side but the altitude)
10. The diagonals create four congruent triangles that reflect upon each other
.
Friday, May 31, 2013
Top Ten Properties of a Rectangle
Top Ten Properties of a Rectangle
1. A rectangle is a quadrilateral so it has four sides.
2. A rectangle is a parallelogram
3. The perimeter of a rectangle equals 2(base X height)
4. The area of a rectangle equals base X height
5. Opposite sides of a rectangle are congruent
6. A rectangle has four right angles
7. The diagonal of a rectangle is the hypotenuse of a right triangle
8. Opposite sides of a rectangle are parallel
9. The diagonals of a rectangle do not intersect in a right angle.
10. The diagonals of a rectangle create opposite central angles that are congruent.
Thursday, May 30, 2013
Complementary and Supplementary Angles
What are complementary and supplementary angles?
Complementary angles are two angles that add to ninety degrees.
Supplementary angles are two angles that add to one hundred and eighty degrees.
Sample problem one.
30 is the complement of what angle?
Step 1 30 + X = 90◦
Step 2 Subtract 30 from each side x= 60◦
Sample problem 2 What is the angle measure of X ?
Step 1 In a right triangle the two angles are complementary.
Step 2 90 – 68= 22◦
Sample problem 3
105◦ is the supplement of what angle?
Step 1 x + 105 = 180
Step 2 subtract 105 from each side x = 75◦
Sample problem 4
What is the angle measure of ∠x ?
Step 1 A straight line measures 180◦
Step 2 180 -65 = 115◦ is the measure of ∠x
Tuesday, May 21, 2013
Finding the surface area of a Cone
How to find the surface area of a Cone
The video works the problem Surface Area of a Cone
In order to find the surface area of a cone you add the lateral area plus the base area
The lateral area of a cone equals 1/2 dπ*s
D = diameter
S = slant height
Base Area = πr^2
Find the surface area of a cone with a diameter of 6 units and a height of 4 units.
Step 1. The radius = ½ diameter = 3 units
Step 2 Find the slant height by using the Pythagorean Theorem a^2+b^2=c^2
Use the height and radius to find the slant height 3^2+4^2=c^2 which equals 9 +16 = 25
√25=5 equals your slant height
Step 3 Now use 1/2 dπ*s
1/2 6Ï€*5=3Ï€*5=15Ï€ which will equals the lateral area
Step 4. Find the base area by using πr^2
π3^2 = π9
Step 5 Add the lateral and base area in order to get surface area
15π+9 π=24π units^2
Check out the Video if confused Surface Area of a Cone
Sunday, May 19, 2013
How to find the perimeter of a parallelogram
Perimeter of a Parallelogram
Watch the video to see each problem worked out
In order to find the perimeter of a parallelogram you can use two methods.
Method 1 Perimeter of parallelogram equals, add all four sides
Method 2 Perimeter of parallelogram equals 2 l +2w l = length w = width
Problem 1 Find the perimeter of a parallelogram with a side of 3 units and 10 units.
Step 1. The opposite sides of a parallelogram are congruent. Therefore, if you know the length of one side you know the length of the other.
Step 2. Add all four sides 3+3+10+10=26 units or (2*3) + (2*10) = 6+20=26 units
Problem 2 Find the perimeter of a parallelogram with a side of 8 units and a height of 6 units and an angle measure of 60 degrees.
Step 1 Use the altitude to find the length of the missing side.
Step 2 The altitude creates a 30-60-90 triangle. If you find the hypothesis of the 30-60-90 Triangle this will be the length of the missing side.
Step 3 The height becomes the long leg which equals x√(3 ) x = the length of the short leg
Since you know the length of the long leg you can use 6=x√3
Step 3A 6/√3 = √3/√3
Step 3B (6√3)/2 =2√3
Step 4 Now that I know x I can use 2x to find the hypotenuse
2*2√(3 ) =4√3
Step 5. Now use the perimeter formula for a parallelogram 2l + 2w
2*8 + 2*4√3
16 + 8√3 this is your final answer because you can add a constant and a radical
Wednesday, May 15, 2013
Perimeter of a rhombus
Finding the perimeter of a rhombus
The video works out each problem
Let’s look at finding the perimeter of a rhombus. The perimeter is the distance around the outside of an object. A rhombus is similar to a square with a couple of unique features. They are both quadrilaterals but a rhombus doesn’t have right angles at the corners. Like a square a rhombus has congruent sides, so the perimeter formula is the same as a square, which is 4 times one side length.
Perimeter = 4s s=side
Problem 1. What is the perimeter of a rhombus with a side of 5 units?
The video works the problem
Step 1. Use 4s
Step 2 4*5= 20 units Perimeter is linear, therefore it is not squared
Let’s next look at a problem a little more involved.
Find the perimeter of a rhombus with a diagonal of 10 units and measure of angle ABC equals 120 degrees.
Step 1. The diagonals of a rhombus are perpendicular to each other so they form right angles. These right angles create a right triangle.
Step 2. The diagonal also bisects each other and divide each other in half. The 10 unit diagonal is divided into two 5 unit lines Combine step one and two and you have a 30-60-90 right triangle with a short leg of 5 units .
Step 3. In order to find the side of the rhombus I will find the hypotenuse of the right triangle. The formula for the hypotenuse of a right triangle equals 2x
Step 4. We know x = 5 units from the diagonal being bisected by the other diagonal so it is 5 units.
So the hypotenuse equals 2*5 = 10 units
Step 5. Now use the perimeter formula of 4s which equals 4* 10 = 40 units
Saturday, May 11, 2013
Finding the perimeter of a rectangle.
How to find the perimeter of a rectangle.
The video link below works each problem. Hope it helps in class.
How to find the perimeter of a rectangle
Let’s look at the step by step procedure for finding the perimeter of a rectangle. First we need to look at some rectangle properties. A rectangle has opposite sides that are equal and four right angles. Therefore if you know the length of one side then the opposite side will be the same length. The right angles allow the diagonal to divide the rectangle into a right triangle.
Example problem 1. Find the perimeter of a rectangle with one side of 8 units and one side of 12 units.
Step 1. Find the length of the two missing sides, this is easy because opposite sides are congruent so the four sides are 8, 8, 12, 12 units.
Step 2. Add the side lengths together.
8+8+12+12=40 units
Step 3. Another method to find the perimeter of a rectangle is to use 2*length + 2* Width
2*8 + 2*12
16 + 24 = 40 units
Example problem 2. Find the perimeter if you have a rectangle with a diagonal of 13 units and a side length of 12 units.
Step 1. Because a rectangle has four right angles the diagonal creates a right triangle with the diagonal being the hypotenuse of the right triangle.
Step 2. Use the Pythagorean Theorem to find the length of the missing side. Let’s label c=13 (the diagonal) a = 12 (the side length we are given) and solve for b
Step 3. Use the Pythagorean Theorem a^2+b^2=c^2
Step a.12^2+b^2=13^2
Step b.144+b^2=169 (Subtract 144 from each side.
Step c. b^2=25
Step d. b=√(25 ) b=5 units
Step 4. Now we know the missing side so I can use the formula for the perimeter of a rectangle
2*length + 2*width = perimeter
2*5 + 2*12 = 10 +24= 34 units
Thursday, May 9, 2013
How to find the area of a square.
How to find the area of a square ?
Please watch the video if you need to watch the problems being solved
Let’s begin with the formula for area of a square is s^2 s=side
Example 1 Find the area of a square with a side of 8 units.
Step 1 Plug the number into the formula: 8^(2 )=64 units^2
Let’s look at an example using diagonals.
Example 2 Find the area of a square with a diagonal of 14 units.
Step 1. The diagonal bisects the ninety degree angle and creates a 45-45-90 triangle. We can use the rules of a 45-45-90 triangle to find the length of one side.
Step 2. The leg lengths of a 45-45-90 triangle equals x and the hypotenuse equals x√2
Step 3. In order to get x by itself I will take the hypotenuse length of the 45-45-90 triangle that the diagonal creates 14 and set it equal to x root 2 which looks like
14=x√2
Step 4. Solve for x by dividing by the √2
14/√2=(x√2)/√2 =7√2 = S
Step 5.Now we plug s into our area formula for a square s^2
Step 6. (7√(2 ) )^2 = 42 x2 =98 units^2
Tuesday, May 7, 2013
What is so special about a 45-45-90 triangle?
What is so special about a-45-90-45 Triangle?
A 45-45-90 triangle is classified as a special right triangle, but why is it special? Let’s look at the special rules of a 45-45-90 Triangle.
Rule 1. If you know the length of one leg you know the length of the other leg because they are equal.
Rule 2. In order to find the length of the hypotenuse multiply the leg length times the square root of two. This would be written x√2 where x=leg length
Rule 3. In order to find the leg length divide your hypotenuse by the square root of 2.
Rule 4 .The area of a 45-45-90 triangle equals 1/2(leg)^2
Let’s look at two examples.
Example 1 Find the hypotenuse of a 45-45-90 triangle with leg length of 7 units.
Step 1. Use x√(2 )
Step 2. 7√(2 ) units
Example2. What is the length of one leg of a 45-45-90 triangle if you have a hypotenuse with a length of 12 units?
Step 1. 12/√2 use the formula for leg length hypotenuse divided by square root two
Step 2. 12/√2* √2/√2
Step 3. (12√2)/2 =6√2
Thursday, May 2, 2013
What is a Quadrilateral?
What is a quadrilateral? The key to a quadrilateral is found in its name, “quad" meaning four and “lateral" meaning side. So a quadrilateral is a four sided polygon. Some common examples are kites, parallelograms, trapezoids, rhombuses, rectangles, and squares.
The following video goes over the properties of a Quadrilateral
Properties of a Quadrilateral
• Four Sided
• Closed figure
• Four vertices (also known as corners)
• Interior angles add up to 360◦
• Straight sides, no curves
Two diagonals
Quadrilaterals can be subdivided into parallelograms and trapezoids. Let’s look at parallelograms. Some common examples of parallelograms are rectangles, rhombuses, and squares. They all have opposite sides that are parallel and congruent, and diagonals that bisect each other.
Trapezoids have exactly one pair of parallel sides. The perimeter of a trapezoid is the sum of four side lengths and the area is one half times base one plus base two times height. The perimeter and area of each quadrilateral varies according to its shape. Here is a link to the perimeter and area formulas for most quadrilaterals.
Tuesday, April 30, 2013
Area of a rectangle
Area of a rectangle
The formula for area of a rectangle is b*h (base times height)
In a rectangle the opposite sides are congruent so if you the measure of one side then you also know the measure of the opposite side.
Please watch the video to see each problem worked out
Here is a list of area formulas plane shapes
Problem 1. Find the area of a rectangle with a base of 10 units and a height of 8 units.
Step 1. Plug the numbers into the formula b*h
8 * 10 =80 units squared
Next, let’s look at one more challenging.
Problem 2. Find the base of a rectangle with an area of 100 units and a height of 5 units.
Step 1. Write the formula for the area of a rectangle Area= b*h
Step 2. Plug in what you know 100 = b * 5
Step 3 Divide each side by 5 100/5= b/5
Step 4. 20 =b and b = the base of the rectangle
Problem 3. Find the area of a rectangle with a diagonal of 15 units and a side of 9 units.
Step 1. Plug in what you know A = b * 9
Step 2. The diagonal divides the rectangle into a right triangle. You can use the Pythagorean Theorem to find the base.
A = 9 c= 15 b=your unknown (see picture below)
9^2+ b^2= 15^2
81+ b^2=225
b^2=144
b=√144
b = 12
Step 3. Use your area formula of a rectangle Area = b*h
Area = 12 * 9 = 108 u^2
Sunday, April 28, 2013
Finding the area of a Trapezoid
Area of a Trapezoid
Here is a link to the video that goes over the two trapezoid area problems.
http://www.youtube.com/watch?v=y0UWiXIaCRw
Let’s first look at where the formula for the area of a trapezoid comes from.
The formula for the area of a trapezoid equals 1/2h(b1 + b2) h=height
First a trapezoid has two parallel bases. If you draw a line top vertex straight down it forms a triangle.
Next, I will rotate the triangle all the way around it forms a rectangle.
The rectangle has the same area as the original trapezoid and the two bases are equal to each other and is equal to the mid segment. Now when you add the two bases together and multiply by ½ you get an average of the two bases and then multiplying this average by the height. So that is where the formula comes from it the mid segment times the height.
Problem 1. Find the area of a trapezoid with a height of 10 units and a base of 12 units and a base of 16 units.
Step 1.Plug in 12 and 16 for b1 and b2
½ 10 (12 + 16)
Step 2. ½ (10 * 28)
Step 3.½(280) = 140 units
Problem 2.Find the area of a trapezoid with bases of 5 and 9 and the length of the leg is 4 units. The angle measure is 60◦.
Step 1.The leg is not your height so you have to find your height.
Since you have a 60◦ angle and a 90◦ angle with the triangle you can take ½ the hypotenuse to get the short leg which equals 2 units ( In a 30,60,90 Triangle the short leg equals 1/2 the hypotenuse)
Next take the length of short leg times 2√3 = the height of the trapezoid
Step 2. Plug in your number in the area formula
½*2√3 ( 5+9)
Step. 3½ * 2√3 ( 14) = ½ 28√3
Step 4.14√3 = units squared equals the area of the trapezoid
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