Calculate Parallelogram Area: Given Perimeter 60 and Height 3

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

AAABBBDDDCCC4X32X

Calculate the area of the parallelogram.

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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
00:04 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

Step-by-step written solution

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1

Understand the problem

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

AAABBBDDDCCC4X32X

Calculate the area of the parallelogram.

2

Step-by-step solution

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

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

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

60=12x 60=12x

x=5 x=5

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

AB=CD=4×5=20 AB=CD=4\times5=20

AC=BD=2×5=10 AC=BD=2\times5=10

Hence the area of the parallelogram will be equal to:

CD×3=20×3=60 CD\times3=20\times3=60

3

Final Answer

60

Practice Quiz

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Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

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