Perimeter of a Parallelogram - Examples, Exercises and Solutions

Given the parallelogram:

Calculate the perimeter of the parallelogram.

As in a parallelogram every pair of opposite sides are equal:

$AB=CD=6,AC=BD=4$

The perimeter of the parallelogram is equal to the sum of all sides together:

$4+4+6+6=8+12=20$

20

Given the parallelogram:

Calculate the perimeter of the parallelogram.

As in a parallelogram each pair of opposite sides are equal and parallel,

It is possible to argue that:

$AC=BD=7$

$AB=CD=10$

Now we can calculate the perimeter of the parallelogram by adding all its sides:

$10+10+7+7=20+14=34$

34

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.

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:

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

42

The longest sides of a parallelogram are X cm long and are four times longer than the shorter sides.

Express the perimeter of the parallelogram in terms of X.

In a parallelogram, each pair of opposite sides are equal and parallel: AB = CD and AC = BD.

Given that the length of one side is 4 times greater than the other side equal to X, we know that:

$AB=CD=4AC=4BD$

Now we replace the data in this equation with out own (assuming that AB = CD = X):

$x=x=4AC=4BD$

We divide by 4:

$\frac{x}{4}=\frac{x}{4}=AC=BD$

Now we calculate the perimeter of the parallelogram and express both AC and BD using X:

$P=x+\frac{x}{4}+x+\frac{x}{4}$

$P=2x+\frac{x}{4}+\frac{x}{4}=2\frac{1}{2}x$

2.5X cm

Look at the parallelogram shown below.

AB = 6

AC = X

The perimeter of the parallelogram is 20.

Find X.

As in a parallelogram each pair of opposite sides are equal:

$AB=CD=6,AC=BD=x$

Calculate X according to the given perimeter:

$20=6+6+x+x$

$20=12+2x$

$20-12=2x$

$8=2x$

$x=4$

4

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

Calculate the area of the parallelogram.

As in a parallelogram each pair of opposite sides are equal to each other:

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

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

$60=12x$

$x=5$

Now we calculate all the sides of the parallelogram:

$AB=CD=4\times5=20$

$AC=BD=2\times5=10$

The area of the parallelogram will be equal to:

$CD\times3=20\times3=60$

60

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.

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:

$CE\times AD=10\times7=70$

70 cm²

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

Given the parallelogram:

Calculate the perimeter of the parallelogram.

22

Given the parallelogram:

Calculate the perimeter of the parallelogram.

18

Given the parallelogram:

Calculate the perimeter of the parallelogram.

14

Given the parallelogram:

Calculate the perimeter of the parallelogram.

24

Given the parallelogram:

Calculate the perimeter of the parallelogram.

50

Given the parallelogram:

Calculate the perimeter of the parallelogram.

36

Given the parallelogram:

Calculate the perimeter of the parallelogram.

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