## What is the perimeter?

The perimeter indicates the distance we will walk if we start from a certain point, complete a full lap, and return exactly to the starting point.
For example, if we are asked what the perimeter of the waist is, we will take a tape measure and measure the perimeter from a certain point until completing a full lap and returning to the same point from which we started the measurement.
It works exactly the same way in mathematics. The perimeter of any shape is the distance from a specific point back to it after having completely surrounded it.
If this is our figure:

Its perimeter will be the distance we cover if we travel along its line from a certain point, and return to it after making a full lap. Imagine that you are surrounding the figure:

## Examples with solutions for Perimeter

### Exercise #1

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

### Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$AB=CD=2$

$AD=BC=7$

Now we can add all the sides together and find the perimeter:

$2+7+2+7=4+14=18$

18 cm

### Exercise #2

Look at the following rectangle:

Find its perimeter.

### Step-by-Step Solution

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

### Exercise #3

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

### Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$AD=BC=9.5$

$AB=CD=1.5$

Now we can add all the sides together and find the perimeter:

$1.5+9.5+1.5+9.5=19+3=22$

22 cm

### Exercise #4

Calculate the perimeter of the given parallelogram:

### Step-by-Step Solution

As is true for 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

### Exercise #5

Calculate the perimeter of the given parallelogram.

### Step-by-Step Solution

As is true for a parallelogram each pair of opposite sides are equal and parallel,

Therefore it is possible to argue that:

$AC=BD=7$

$AB=CD=10$

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

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

34

### Exercise #6

Look at the rectangle below:

Calculate its perimeter.

### Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$AB=CD=10$

$BC=AD=7$

Now let's add all the sides together to find the perimeter of the rectangle:

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

34

### Exercise #7

Look at the trapezoid in the diagram.

What is its perimeter?

### Step-by-Step Solution

To calculate the perimeter, we'll add up all the sides of the trapezoid:

7+10+7+12 =

36

And that's the solution!

36

### Exercise #8

Calculate the perimeter of the parallelogram ABCD.

CD is parallel to AB.

### Step-by-Step Solution

Let's recall the properties of parallelograms, where pairs of opposite sides are parallel and equal.

Therefore, AB is parallel to CD

Therefore, BC is parallel to AD

From this, we can conclude that AB=CD=7

Now we can calculate the perimeter by adding all the sides together:

$7+7+12+12=14+24=38$

38

### Exercise #9

What is the perimeter of the trapezoid in the figure?

### Step-by-Step Solution

To find the perimeter we will add all the sides:

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

24

### Exercise #10

Look at the circle in the figure:

Its radius is equal to 4.

What is its circumference?

### Step-by-Step Solution

The formula for the circumference is equal to:

$2\pi r$

### Exercise #11

Look at the circle in the figure.

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

### Step-by-Step Solution

Formula of the circumference:

$P=2\pi r$

We insert the given data into the formula:

$P=2\times6\times\pi$

$P=12\pi$

$12\pi$

### Exercise #12

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

What is its circumference?

### Step-by-Step Solution

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

### Exercise #13

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

### Step-by-Step Solution

To calculate, we will use the formula:

$\frac{P}{2r}=\pi$

Pi is the ratio between the circumference of the circle and the diameter of the circle.

The diameter is equal to 2 radii.

Let's substitute the given data into the formula:

$\frac{8}{4}=\pi$

$2\ne\pi$

Therefore, this situation is not possible.

Impossible

### Exercise #14

Look at the isosceles triangle below:

What is its perimeter?

### Step-by-Step Solution

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

### Exercise #15

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.

### Step-by-Step Solution

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