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# What Is Perimeter and How Do You Find the Perimeter ?

The perimeter is the length of the outside of any shape. For example, consider a triangle. It has three sides. How do you find the perimeter ? The perimeter can be calculated by measuring each side and then summing them.

How do you find the perimeter another way? Interestingly, if you start walking along the edge the shape, you will walk a total distance equal to the perimeter of the shape. How do you find the perimeter this way? So, for example, you are walking around the swimming pool. Two sides of the pool are 10ft long and two are 5ft long. So, you walked a total of 10ft+10ft+5ft+5ft = 30ft. Therefore, the perimeter of the pool is 30ft.p>

How do you find the perimeter using formulas? Mathematicians have come up with specific formulas to calculate the perimeter of different shapes. Using these formulas, we will share with you how do you find the perimeter then.

## How Do You Find the Perimeter of a Triangle

For any polygon, you can find the perimeter by measuring the total distance of its outer boundary. How do you find the perimeter of a triangle? The same goes for a triangle. You can find the perimeter of a triangle by summing the length of each of its sides.

How do you find the perimeter of a triangle by using formula? The formula for the perimeter of the triangle is given as:

Perimeter = a + b + c

Where a, b, and c are the lengths of the sides of any triangle.

So, let’s suppose you have a triangle from your music class. How do you find the perimeter then? Let’s suppose the lengths come out to be 5cm, 5cm, and 4cm. The perimeter of the triangle is 5cm+5cm+4cm = 14cm.

Similarly, if you have a triangular room, measure the length of the sides. Let’s suppose the lengths are 7ft, 8ft, and 7ft. How do you find the perimeter then? The perimeter of the room is 7ft+8ft+7ft = 22ft.

### Challenge:

We have seen how do you find the perimeter before. A triangle has sides whose lengths are 3x, 4x, and 5x. If the perimeter of a triangle is 24ft, what is the value of x?

Solution:

How do you find the perimeter now? You know that now. Since, the perimeter of a triangle is given by the formula

Perimeter = a + b +c

And here a= 3x, b=4x, and c=5x

Therefore, Perimeter =

Put the value of perimeter in the above equation

24 = 3x + 4x +5x

24 = 12x

12x = 24

x= 2.

Therefore, the value of x is 2.

## How Do You Find the Perimeter of a Rectangle

A rectangle is a polygon with four sides. How do you find the perimeter of a rectangle? The perimeter of a rectangle is the distance around it. In simpler words, the total length of the sides of the rectangle is the perimeter of a rectangle.

For example, consider a rectangle with two sides measured as 4ft and two as 2ft. How do you find the perimeter then? The perimeter of this rectangle is 4ft+4ft+2ft+2ft = 12ft.

How do you find the perimeter of a rectangle using a formula? Mathematically, the formula of the perimeter of a rectangle can be given as

Perimeter = 2 length + 2 width

So, for the example we did above, the length of the rectangle is 4ft and the width is 2ft. How do you find the perimeter using mathematical formula?

Using the above formula we get,

Perimeter = 2 x 4 + 2 x 2

Perimeter = 12ft

Now, let’s suppose the size of the rectangle is doubled. How do you find the perimeter now? The perimeter will now be double as well. So,

New perimeter = 2 x old perimeter

New perimeter = 2 x 12

New perimeter = 24ft

How do you find the perimeter and compare them? Two different rectangles can have the same perimeter. For example, the length and width of a rectangle is 3ft and 2ft. The length and width of another rectangle is 1ft and 4ft. How do you find the perimeter of the rectangles?

Perimeter of the rectangle = 2 length + 2 width

Perimeter of the first rectangle = 2 x 3 + 2 x 2

Perimeter of the first rectangle = 10ft

And,

Perimeter of the second rectangle = 1 x 2 + 2 x 4

Perimeter of the second rectangle = 10ft

## How Do You Find the Perimeter of a Square?

A square is a polygon with four sides. It belongs to the family of quadrilaterals. A square is a special case of a rectangle. All of its sides are equal; therefore, knowing the length of one side is enough to determine any measurement. How do you find the perimeter now?

Again, the concept of the perimeter remains the same. Perimeter of a square is the distance around a square. So, if a square has sides equal to 2cm, how do you find the perimeter of the square? The perimeter of this square will be the sum of all sides, that is, 2cm+2cm+2cm+2cm = 8cm.

How do you find the perimeter of a square using a formula? The formula for the perimeter of a square is given as

Perimeter of a square = 4 x side

So, for the above example, the perimeter of the square using the above formula can be found by

Perimeter = 4 x 2

Perimeter = 8cm

## How Do You Find the Perimeter of a Compound Shape?

In order to find the perimeter of a compound shape, consider the following figure:

How do you find the perimeter of a shape that is not a triangle, rectangle, or a square? There are two methods to find its perimeter.

Method 1:

How do you find the perimeter?

Perimeter of a compound shape = sum of all its sides

Perimeter of a compound shape = 2cm+6cm+4cm+8cm+6cm

Perimeter of a compound shape = 28cm

Method 2:

How do you find the perimeter

Draw an imaginary line. Can you spot a square and a rectangle in the figure?

Perimeter of the compound shape = perimeter of square + perimeter of rectangle

Now, apply the formulas you just learnt

Perimeter of the compound shape = (2 x side) + (2 length + 2 width)

Perimeter of the compound shape = (2 x 2) + (2 x 8 + 2 x 4)

Perimeter of the compound shape = 4 + 24

Perimeter of the compound shape = 28cm

## How Do You Find the Perimeter of a Polygon with More Sides?

Polygons can be of more than four sides. These are pentagons, hexagons etc. How do you find the perimeter of these polygons? Well, the concept remains the same. You need to sum the lengths of all sides to obtain the perimeter.

A pentagon is a polygon with five sides and a hexagon is a polygon with six sides. The sides of a regular hexagon are equal in length. How do you find the perimeter of the hexagon? For example, the length of the sides of the hexagon is 5cm, the perimeter will be

Perimeter of a hexagon = 5cm+5cm+5cm+5cm+5cm+5cm

Perimeter of a hexagon = 30cm

How do you find the perimeter of a hexagon using a formula? The formula for the perimeter of a hexagon is given as

Perimeter of a hexagon = 6 x side

Perimeter of a hexagon = 6 x 5

Perimeter of a hexagon = 30cm

## How Do You Find the Perimeter of a Circle?

A circle is a geometrical shape that consists of points that are at equal distance from the centre of the shape. For example a CD. How do you find the perimeter of a circle?

The perimeter of a circle can be determined both manually and through formulas.

How do you find the perimeter of a circle manually? If you are given a circle, and you need to find the perimeter of that circle, take a thread and wrap it around the circle. Now cut off the extra portion. Next, measure the length of the thread that you wrapped around the circle. So you see how do you find the perimeter now?

Of course, you can’t carry around a piece of thread to calculate the perimeter of a circle. How do you find the perimeter of the circle then? You use the formula.

How do you find the perimeter of the circle using a formula? The formula for the perimeter of a circle is given as

Perimeter of a circle = 2 x pi x r

Where pi = 22/7 or 3.142 and r is the radius of the circle.

The perimeter of the circle is called the circumference.

The radius is the distance from any point on the edge of the circle to the centre. It remains the same regardless of the point you choose.

So, for a circle with radius r = 2cm, how do you find the perimeter then?

Perimeter of the circle = circumference = 2 x pi x r

Circumference = 2 x 22/7 x 2

Circumference = 12.57cm

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