Calculate Parallelogram Area: Given Perimeter 60 and Height 3

Question

Below is a parallelogram with a perimeter of 60 and a height of 3.

Calculate the area of the parallelogram.

00:00 Calculate the area of the parallelogram

00:04 Opposite sides are equal in a parallelogram

00:16 Let's substitute the side values

00:29 The perimeter of the parallelogram equals the sum of its sides

00:42 Let's substitute appropriate values and solve for X

01:07 This is the value of X

01:11 Now let's use the formula for calculating the area of a parallelogram

01:15 Side (CD) multiplied by the height to side (H)

01:22 Let's substitute appropriate values and solve for the area

01:38 Let's substitute the X value we found earlier

01:47 And this is the solution to the problem

As is true for a parallelogram each pair of opposite sides are equal to one other:

$AB=CD=4x,AC=BD=2x$

To begin we will find X through the perimeter: $60=2x+4x+2x+4x$

$60=12x$

$x=5$

Next we will calculate all of the sides of the parallelogram:

$AB=CD=4\times5=20$

$AC=BD=2\times5=10$

Hence the area of the parallelogram will be equal to:

$CD\times3=20\times3=60$