Calculate Parallelogram Area: 38cm Perimeter with Proportional Sides

Question

ABCD is a parallelogram with a perimeter of 38 cm.

AB is twice as long as CE.

AD is three times shorter than CE.

CE is the height of the parallelogram.

Calculate the area of the parallelogram.

Video Solution

Solution Steps

00:00 Calculate the area of the parallelogram

00:03 Let's mark the height with X

00:07 Side lengths according to the given data, we'll express the sides using X

00:19 The perimeter of the parallelogram equals the sum of its sides

00:29 Opposite sides are equal in a parallelogram

00:34 We'll substitute appropriate values and solve for X

00:49 Pay attention to proper parentheses

00:56 Isolate X

01:02 And this is the height X

01:10 Now let's substitute X value to find side AD

01:14 Now we can calculate the parallelogram's area

01:19 Multiply height(EC) by side(AD)

01:23 And this is the solution to the question

Step-by-Step Solution

Let's call CE as X

According to the data

$AB=x+2,AD=x-3$

The perimeter of the parallelogram:

$2(AB+AD)$

$38=2(x+2+x-3)$

$38=2(2x-1)$

$38=4x-2$

$38+2=4x$

$40=4x$

$x=10$

Now it can be argued:

$AD=10-3=7,CE=10$

The area of the parallelogram:

$CE\times AD=10\times7=70$

Answer

70 cm²

Related Subjects

Parallelogram The area of a parallelogram: what is it and how is it calculated? Perimeter of a Parallelogram Area Perimeter

Question Types

Area of a Parallelogram: Finding Area based off Perimeter and Vice Versa Perimeter of a Parallelogram: Finding Area based off Perimeter and Vice Versa