Calculate Parallelogram Area: 38cm Perimeter with Proportional Sides

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.

AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

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1

Understand the problem

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.

AAABBBCCCDDDEEE

2

Step-by-step solution

Let's call CE as X

According to the data

AB=x+2,AD=x−3 AB=x+2,AD=x-3

The perimeter of the parallelogram:

2(AB+AD) 2(AB+AD)

38=2(x+2+x−3) 38=2(x+2+x-3)

38=2(2x−1) 38=2(2x-1)

38=4x−2 38=4x-2

38+2=4x 38+2=4x

40=4x 40=4x

x=10 x=10

Now it can be argued:

AD=10−3=7,CE=10 AD=10-3=7,CE=10

The area of the parallelogram:

CE×AD=10×7=70 CE\times AD=10\times7=70

3

Final Answer

70 cm²

Practice Quiz

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A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

6664.54.54.5

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