Examples with solutions for Area of a Parallelogram: Calculate The Missing Side based on the formula

Exercise #1

Look at the parallelogram in the figure.

Its area is equal to 70 cm².

Calculate DC.

555AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

The formula for the area of a parallelogram:

Height * The side to which the height descends.

We replace in the formula all the known data, including the area:

5*DC = 70

We divide by 5:

DC = 70/5 = 14

And that's how we reveal the unknown!

Answer

14 14 cm

Exercise #2

Look at the parallelogram in the figure below.

Its area is equal to 40 cm².

Calculate AE.

888AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

We are told that ABCD is a parallelogram,AB=CD=8 AB=CD=8 According to the properties of a parallelogram, each pair of opposite sides are equal and parallel.

Hence to find AE we will need to use the area given to us in the formula in order to determine the area of the parallelogram:

S=DC×AE S=DC\times AE

40=8×AE 40=8\times AE

We divide both sides of the equation by 8:

8AE:8=40:8 8AE:8=40:8

AE=5 AE=5

Answer

5 5 cm

Exercise #3

Below is the parallelogram ABCD.

Its area is equal to 100 cm².

Calculate the length of side AD.

666AAABBBCCCDDDEEE

Video Solution

Answer

16.67 16.67 cm

Exercise #4

Given the parallelogram of the figure

The height of the side AD equal to 4 cm

The area of the parallelogram is equal to 40 cm².

Find AD

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Video Solution

Answer

10 10 cm

Exercise #5

The parallelogram ABCD has an area equal to 60 cm².

Calculate the length of BE.

121212AAABBBCCCDDDEEE

Video Solution

Answer

5 5 cm

Exercise #6

The area of parallelogram ABCD is 88 cm².

Calculate the length of side DC.

888AAABBBCCCDDDEEE

Video Solution

Answer

11 11 cm

Exercise #7

Calculate X based on the data in the figure:

S=21S=21S=21333XXX

Video Solution

Answer

7

Exercise #8

Calculate X based on the data from the figure:

S=45S=45S=45XXX555

Video Solution

Answer

9

Exercise #9

Look at the parallelogram ABCD.

The area ABCD is 60 cm².
AD=8 AD=8

Calculate the height of ABCD.

S=60S=60S=60888AAABBBCCCDDD

Video Solution

Answer

7.5

Exercise #10

Calculate the area of the parallelogram ABCD using the following data:

The area of ABCD is 40 cm².

BC=5 BC=5

AB=8 AB=8

S=40S=40S=40888555AAABBBCCCDDDEEE

Video Solution

Answer

5

Exercise #11

ABCD is a parallelogram.

The area is equal to 30 cm².

Calculate AD.

333AAABBBCCCDDDEEE

Video Solution

Answer

It is not possible to calculate.

Exercise #12

Look at the parallelogram of the figure.

Its area is equal to 156 cm².

Calculate AB.

121212AAABBBCCCDDDE

Video Solution

Answer

13 13 cm

Exercise #13

ABCD is a parallelogram.

DC is equal to 4 cm.

The area of the parallelogram is 82 cm².

Work out AE.

444AAABBBCCCDDDEEE

Video Solution

Answer

2012 20\frac{1}{2} cm

Exercise #14

The parallelogram ABCD is shown below.

Its area is equal to 63 cm².

Calculate side AE.

777AAABBBCCCDDDEEE

Video Solution

Answer

It is not possible to calculate.

Exercise #15

Look at the parallelogram ABCD.

Calculate DF using the following:

AB=8 AB=8

BC=16 BC=16

BE=10 BE=10

161616888101010BBBCCCDDDAAAEEEFFF

Video Solution

Answer

20

Exercise #16

Using the data from the figure, calculate X:

S=36S=36S=36333222XXX

Video Solution

Answer

10

Exercise #17

Look at the parallelogram ABCD.

The area of ABCD is 4x 4x .

AE AE is the height of the parallelogram.

AE=2 AE=2

Calculate AD.

S=4XS=4XS=4X222DDDCCCBBBAAAEEE

Video Solution

Answer

2X

Exercise #18

The area of the parallelogram below is 56.

BE is its height.

Calculate x.

x+5x+5x+5x-5x-5x-5AAADDDCCCBBBEEE

Video Solution

Answer

9 9