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

Question 1

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.

Question 2

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

Calculate the area of the parallelogram.

Question 3

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.

Question 4

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

Question 5

ABCD is a parallelogram whose perimeter is equal to 22 cm.

AC=4 height of the parallelogram for side CD is 3 cm

Calculate the area of the parallelogram

Examples with solutions for Perimeter of a Parallelogram: Finding Area based off Perimeter and Vice Versa

Exercise #1

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.

Video Solution

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:

$AB\times h=S$

$AB\times3=39$

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

$AB=13$

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

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

Answer

Exercise #2

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

Calculate the area of the parallelogram.

Video Solution

Step-by-Step Solution

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

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

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

$60=12x$

$x=5$

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

$AB=CD=4\times5=20$

$AC=BD=2\times5=10$

Hence the area of the parallelogram will be equal to:

$CD\times3=20\times3=60$

Answer

Exercise #3

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

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

Exercise #4

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

Video Solution

Step-by-Step Solution

The perimeter of the parallelogram is calculated as follows:

$S_{ABCD}=AB+BC+CD+DA$ Since ABCD is a parallelogram, each pair of opposite sides is equal, and therefore, AB=DC and AD=BC

According to the figure that the side of the parallelogram is 2 times larger than the side adjacent to it, it can be argued that $AB=DC=2BC$

We inut the data we know in the formula to calculate the perimeter:

$P_{ABCD}=2BC+BC+2BC+BC$

We replace the given perimeter in the formula and add up all the BC coefficients accordingly:

$24=6BC$

We divide the two sections by 6

$24:6=6BC:6$

$BC=4$

We know that $AB=DC=2BC$ We replace the data we obtained (BC=4)

$AB=DC=2\times4=8$

As ABCD is a parallelogram, then all pairs of opposite sides are equal, therefore BC=AD=4

To find EC we use the formula: $A_{ABCD}=AB\times EC$

We replace the existing data:

$24=8\times EC$

We divide the two sections by 8 $24:8=8EC:8$

$3=EC$

Answer

3 cm

Exercise #5

ABCD is a parallelogram whose perimeter is equal to 22 cm.

AC=4 height of the parallelogram for side CD is 3 cm

Calculate the area of the parallelogram

Video Solution

Answer

21 cm².

Question 1

A parallelogram has an area of 40 cm².

AC = 6 cm

Height of the rectangle = 5 cm

Calculate the perimeter of the parallelogram.

Question 2

A parallelogram has an area of 14 cm².

AC = 3 cm

Height = 2 cm

Calculate the perimeter of the parallelogram.

Question 3

Given the parallelogram whose area is equal to 35 cm² and AC=6 cm and the height of the rectangle = 5 cm:

Calculate the perimeter of the parallelogram.

Question 4

Given the parallelogram whose area is equal to 36 cm² and AC=5 cm and the height of the rectangle = 4 cm:

Calculate the perimeter of the parallelogram.

Question 5

Given the parallelogram whose area is equal to 60 cm² and AC=7 cm and the height of the rectangle = 5 cm:

Calculate the perimeter of the parallelogram.

Exercise #6

A parallelogram has an area of 40 cm².

AC = 6 cm

Height of the rectangle = 5 cm

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #7

A parallelogram has an area of 14 cm².

AC = 3 cm

Height = 2 cm

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #8

Given the parallelogram whose area is equal to 35 cm² and AC=6 cm and the height of the rectangle = 5 cm:

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #9

Given the parallelogram whose area is equal to 36 cm² and AC=5 cm and the height of the rectangle = 4 cm:

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #10

Given the parallelogram whose area is equal to 60 cm² and AC=7 cm and the height of the rectangle = 5 cm:

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Question 1

Given the parallelogram whose area is equal to 50 cm² and AC=5 cm and the height of the rectangle = 4 cm:

Calculate the perimeter of the parallelogram.

Question 2

Given the parallelogram whose area is equal to 30 cm² and AC=4 cm and the height of the rectangle = 3 cm:

Calculate the perimeter of the parallelogram.

Question 3

A parallelogram has an area measuring 40 cm².

AC = 6 cm

Height of the rectangle = 5 cm

Calculate the perimeter of the parallelogram.

Question 4

ABCD is a parallelogram whose perimeter is equal to 22 cm.

Side AB is smaller by 5 than side AD

The height of the parallelogram for the side AD is 2 cm

What is the area of the parallelogram?

Question 5

The parallelogram below has a perimeter of 36 cm and a height of 5 cm.

Calculate the area of the parallelogram.

Exercise #11

Given the parallelogram whose area is equal to 50 cm² and AC=5 cm and the height of the rectangle = 4 cm:

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #12

Given the parallelogram whose area is equal to 30 cm² and AC=4 cm and the height of the rectangle = 3 cm:

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #13

A parallelogram has an area measuring 40 cm².

AC = 6 cm

Height of the rectangle = 5 cm

Calculate the perimeter of the parallelogram.

Video Solution

Answer

Exercise #14

ABCD is a parallelogram whose perimeter is equal to 22 cm.

Side AB is smaller by 5 than side AD

The height of the parallelogram for the side AD is 2 cm

What is the area of the parallelogram?

Video Solution

Answer

16 cm²

Exercise #15

The parallelogram below has a perimeter of 36 cm and a height of 5 cm.

Calculate the area of the parallelogram.

Video Solution

Answer

Question 1

A parallelogram has a perimeter of 48 cm and a height of 4 cm.

Calculate the area of the parallelogram.

Question 2

Shown below is a parallelogram which has a perimeter of 24 and a height of 2 cm.

Calculate the area of the parallelogram.

Question 3

A parallelogram has a perimeter of 50 cm and a height of of 2.5 cm.

Calculate the area of the parallelogram.

Question 4

Below is a parallelogram with a perimeter equal to 25 and a height of 3.

Calculate the area of the parallelogram.

Question 5

Below is a parallelogram with a perimeter of 60 and a height of 7 cm.

Calculate the area of the parallelogram.

Exercise #16

A parallelogram has a perimeter of 48 cm and a height of 4 cm.

Calculate the area of the parallelogram.

Video Solution

Answer

Exercise #17

Shown below is a parallelogram which has a perimeter of 24 and a height of 2 cm.

Calculate the area of the parallelogram.

Video Solution

Answer

Exercise #18

A parallelogram has a perimeter of 50 cm and a height of of 2.5 cm.

Calculate the area of the parallelogram.

Video Solution

Answer

Exercise #19

Below is a parallelogram with a perimeter equal to 25 and a height of 3.

Calculate the area of the parallelogram.

Video Solution

Answer

22.5

Exercise #20

Below is a parallelogram with a perimeter of 60 and a height of 7 cm.

Calculate the area of the parallelogram.

Video Solution

Answer

175