Calculate Parallelogram Perimeter: Given Area 39 cm² and Height 3 cm

Question

Given the parallelogram whose area is equal to 39 cm² and AC=8 cm and the height of the rectangle is 3 cm:

Calculate the perimeter of the parallelogram.

00:00 Calculate the perimeter of the parallelogram

00:03 We'll use the formula to calculate the area of a parallelogram

00:07 Side (CD) multiplied by height (H)

00:11 We'll substitute appropriate values and solve to find CD 00:1

00:16 Let's isolate CD

00:28 And this is the length of side CD

00:33 Opposite sides are equal in a parallelogram

00:50 The perimeter of the parallelogram equals the sum of its sides

01:01 We'll substitute appropriate values and solve for the perimeter

01:10 And this is the solution to the question

The area of a parallelogram is equal to the side multiplied by the height of that side.

First, find the value of AB using the parallelogram area formula:

$AB\times h=S$

$AB\times3=39$

$\frac{3AB}{3}=\frac{39}{3}$

$AB=13$

Since in a parallelogram all pairs of opposite sides are equal and parallel, we can find the perimeter of the parallelogram:

$2AB+2AC=2\times13+2\times8=26+16=42$