Area of a Parallelogram: Using variables

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

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$24:8=8EC:8$

$3=EC$

3 cm

Calculate X based on the data from the figure:

9

Calculate X based on the data in the figure:

7

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

21 cm².

Given the parallelogram of the figure

What is your area?

$12xy$

The area of the parallelogram ABCD is 392 cm².

Calculate X.

$7$ cm

Below is the parallelogram ABCD.

AD = 2X

DC = 1.5X

FC = 7

Calculate AE.

$9\frac{1}{3}$ cm

Look at the parallelogram ABCD.

The area of ABCD is $4x$.

$AE$ is the height of the parallelogram.

$AE=2$

Calculate AD.

2X

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

$DA=11$

$AB=20$

$AE=x$

20X

Using the data from the figure, calculate X:

10

The area of parallelogram ABCD is 72Y cm².

Calculate DC.

$8y$

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?

16 cm²

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.

$x^2$

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?

$72\frac{a}{\pi}$ cm²