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

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

AAABBBDDDCCC8393

Calculate the perimeter 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 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

Step-by-step written solution

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1

Understand the problem

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

AAABBBDDDCCC8393

Calculate the perimeter of the parallelogram.

2

Step-by-step solution

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×h=S AB\times h=S

AB×3=39 AB\times3=39

3AB3=393 \frac{3AB}{3}=\frac{39}{3}

AB=13 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=2×13+2×8=26+16=42 2AB+2AC=2\times13+2\times8=26+16=42

3

Final Answer

42

Practice Quiz

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Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

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