Examples with solutions for Area of a Parallelogram: Using variables

Exercise #1

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

AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

The perimeter of the parallelogram is calculated as follows:

SABCD=AB+BC+CD+DA 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 thatAB=DC=2BC AB=DC=2BC

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

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

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

24=6BC 24=6BC

We divide the two sections by 6

24:6=6BC:6 24:6=6BC:6

BC=4 BC=4

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

AB=DC=2×4=8 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:AABCD=AB×EC A_{ABCD}=AB\times EC

We replace the existing data:

24=8×EC 24=8\times EC

We divide the two sections by 824:8=8EC:8 24:8=8EC:8

3=EC 3=EC

Answer

3 cm

Exercise #2

Calculate X based on the data in the figure:

S=21S=21S=21333XXX

Video Solution

Answer

7

Exercise #3

Calculate X based on the data from the figure:

S=45S=45S=45XXX555

Video Solution

Answer

9

Exercise #4

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

444AAABBBDDDCCC

Video Solution

Answer

21 cm².

Exercise #5

Below is the parallelogram ABCD.

AD = 2X

DC = 1.5X

FC = 7

Calculate AE.

1.5X1.5X1.5X777AAABBBCCCDDDFFFEEE2X

Video Solution

Answer

913 9\frac{1}{3} cm

Exercise #6

Given the parallelogram of the figure

What is your area?

3X3X3X4Y4Y4YAAABBBCCCDDDEEE

Video Solution

Answer

12xy 12xy

Exercise #7

The area of the parallelogram ABCD is 392 cm².

Calculate X.

2X2X2X4X4X4XAAABBBCCCDDDEEE

Video Solution

Answer

7 7 cm

Exercise #8

Using the data from the figure, calculate X:

S=36S=36S=36333222XXX

Video Solution

Answer

10

Exercise #9

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 #10

Calculate the area of the parallelogram ABCD according to the following data:

DA=11 DA=11

AB=20 AB=20

AE=x AE=x

111111202020XXXDDDAAABBBCCCEEE

Video Solution

Answer

20X

Exercise #11

The area of parallelogram ABCD is 72Y cm².

Calculate DC.

999AAABBBCCCDDDEEE

Video Solution

Answer

8y 8y

Exercise #12

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?

AAABBBCCCDDD

Video Solution

Answer

16 cm²

Exercise #13

Look at the parallelogram in the figure below.

The length of the height and side AB have a ratio of 4:1.

Express the area of the parallelogram in terms of X.

2X2X2XAAABBBCCCDDD

Video Solution

Answer

x2 x^2

Exercise #14

The circumference of the circle in the diagram is 36a2 36a^2 cm.

BO is the radius.

ABCD is a parallelogram.
BO is perpendicular to DC.

DC = 4a \frac{4}{a}

What is the area of the parallelogram?

BBBOOOCCCDDDAAA

Video Solution

Answer

72aπ 72\frac{a}{\pi} cm²