Area of a Parallelogram: Using variables

Using congruence and similarityUsing external heightUsing Pythagoras' theoremCalculating in two waysVerifying whether or not the formula is applicableUsing ratios for calculationUsing additional geometric shapesFinding Area based off Perimeter and Vice VersaCalculate The Missing Side based on the formulaApplying the formula
Question 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

Question 2

Calculate X based on the data from the figure:

S=45S=45S=45XXX555

Question 3

Calculate X based on the data in the figure:

S=21S=21S=21333XXX

Question 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

Question 5

Below is the parallelogram ABCD.

AD = 2X

DC = 1.5X

FC = 7

Calculate AE.

1.5X1.5X1.5X777AAABBBCCCDDDFFFEEE2X

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 from the figure:

S=45S=45S=45XXX555

Video Solution

Answer

9

Exercise #3

Calculate X based on the data in the figure:

S=21S=21S=21333XXX

Video Solution

Answer

7

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

Question 1

Given the parallelogram of the figure

What is your area?

3X3X3X4Y4Y4YAAABBBCCCDDDEEE

Question 2

The area of the parallelogram ABCD is 392 cm².

Calculate X.

2X2X2X4X4X4XAAABBBCCCDDDEEE

Question 3

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

\( DA=11 \)

\( AB=20 \)

\( AE=x \)

111111202020XXXDDDAAABBBCCCEEE

Question 4

Look at the parallelogram ABCD.

The area of ABCD is \( 4x \).

\( AE \) is the height of the parallelogram.

\( AE=2 \)

Calculate AD.

S=4XS=4XS=4X222DDDCCCBBBAAAEEE

Question 5

The area of parallelogram ABCD is 72Y cm².

Calculate DC.

999AAABBBCCCDDDEEE

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

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 #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

The area of parallelogram ABCD is 72Y cm².

Calculate DC.

999AAABBBCCCDDDEEE

Video Solution

Answer

8y 8y

Question 1

Using the data from the figure, calculate X:

S=36S=36S=36333222XXX

Question 2

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

Question 3

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

Question 4

The circumference of the circle in the diagram is \( 36a^2 \) cm.

BO is the radius.

ABCD is a parallelogram.
BO is perpendicular to DC.

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

What is the area of the parallelogram?

BBBOOOCCCDDDAAA

Exercise #11

Using the data from the figure, calculate X:

S=36S=36S=36333222XXX

Video Solution

Answer

10

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