Perimeter - Examples, Exercises and Solutions

Look at the rectangle below.

Side AB is 4.8 cm long and side AD has a length of 12 cm.

What is the perimeter of the rectangle?

In the drawing, we have a rectangle, although it is not placed in its standard form and is slightly rotated,
but this does not affect that it is a rectangle, and it still has all the properties of a rectangle.
 
The perimeter of a rectangle is the sum of all its sides, that is, to find the perimeter of the rectangle we will have to add the lengths of all the sides.
We also know that in a rectangle the opposite sides are equal.
Therefore, we can use the existing sides to complete the missing lengths.
 
4.8+4.8+12+12 =
33.6 cm

33.6 cm

O is the center of the circle in the figure below.

What is its circumference?

We use the formula:$P=2\pi r$

We replace the data in the formula:$P=2\times8\pi$

$P=16\pi$

$16\pi$ cm

What is the perimeter of the trapezoid in the figure?

To find the perimeter we will add all the sides:

$4+5+9+6=9+9+6=18+6=24$

24

Look at the triangle below:

What is the perimeter of the triangle?

The perimeter of the triangle is equal to the sum of all sides together, therefore:

$6+8+10=14+10=24$

24

Given the triangle:

What is its perimeter?

The perimeter of a triangle is equal to the sum of all its sides together:

$11+7+13=11+20=31$

31

Look at the circle in the figure:

Its radius is equal to 4.

What is its circumference?

The formula for the circumference is equal to:

$2\pi r$

8π

Look at the following rectangle:

Find its perimeter.

Since in a rectangle all pairs of opposite sides are equal:

$AD=BC=5$

$AB=CD=9$

Now we calculate the perimeter of the rectangle by adding the sides:

$5+5+9+9=10+18=28$

28

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

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

Formula of the circumference:

$P=2\pi r$

We replace the data in the formula:

$P=2\times6\times\pi$

$P=12\pi$

$12\pi$

Below is a rectangle composed of two squares.

What is its perimeter?

In a square, all sides are equal. Therefore:
$AB+BC+CD+DE+EF+FA=6$

Thus, we find out what the side AC is equal to:

$AC=AB+BC$

$AB=6+6=12$

In a rectangle, we know that the opposite sides are equal to each other, therefore:

$AB=FD=12$

Therefore, the formula for the perimeter of the rectangle will look like this:

$2\times AB+2\times CD$

We replace the data:

$2\times12+2\times6=$

$24+12=36$

36

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

$5\times1.5=7.5$

Now we will add up all the sides to find the perimeter:

$2+5+3+7.5=7+3+7.5=10+7.5=17.5$

17.5

Given an equilateral triangle:

What is its perimeter?

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

$5+5+5=15$

15

Below is an equilateral triangle:

If the perimeter of the triangle is 33 cm, then what is the value of X?

We know that in an equilateral triangle all sides are equal.

Therefore, if we know that one side is equal to X, then all sides are equal to X.

We know that the perimeter of the triangle is 33.

The perimeter of the triangle is equal to the sum of the sides together.

We replace the data:

$x+x+x=33$

$3x=33$

We divide the two sections by 3:

$\frac{3x}{3}=\frac{33}{3}$

$x=11$

11

Look at the isosceles triangle below:

What is its perimeter?

Since we are referring to an isosceles triangle, the two legs are equal to each other.

In the drawing, they give us the base which is equal to 4 and one side is equal to 6, therefore the other side is also equal to 6.

The perimeter of the triangle is equal to the sum of the sides and therefore:

$6+6+4=12+4=16$

16