How to find the Area of a Parallelogram

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