Finding the area of a circle and the sector area

The video explains how to find the area of a sector and how to find the sector area of a circle. Please see the video guide for more detail.

Circles part 2 lesson 4

Video Guide
00:13 Definition of a sector
00:35 Formula for area of a circle
00:40 Sample problem- finding the area of a circle when given the radius
01:26 Sample problem - finding the area of a circle when given the diameter
02:21 Formula for area of a sector reviewed and explained
03:48 Sample problem - find the area of a sector
04:50 Sample problem - find the area of a sector
06:29 Sample problem- find the area of a circle given the sector area
09:20 Sample problem - find the radius of a circle given a central angle and the sector area

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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