# Perimeter

The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle. Area and perimeter are the two major properties of a 2D shape, which describes them.

The perimeter of each shape varies as per their dimensions. Only in the case of a circle, the perimeter is stated as the circumference of the circle. But the method to find the perimeter of all the polygons is the same, which is we need to add all its sides.

If we need to calculate the length of a circular or rectangular field, then with the help of the perimeter formula we can easily find it, given the dimensions. Let us learn here formula to find perimeter for all the two-dimensional shapes.

## Perimeter Meaning

The perimeter of any two-dimensional closed shape is the total distance around it. Perimeter is the sum of all the sides of a polygon, such as:

• Perimeter of square = Sum of all four sides
• Perimeter of rectangle = Sum of all four sides
• Perimeter of triangle = Sum of all three sides

## Formula

Here is the list of formulas of the perimeter for all the 2d-shapes.

 Name of the Shape Perimeter Formula Circle 2πr Triangle a+b+c, where a,b and c are the sides of triangle Square 4a, where a is the length of side of square Rectangle 2(L+B), where L is length and B is breadth Quadrilateral Sum of all four sides: a+b+c+d Parallelogram 2(a+b), where a and b are adjacent sides Any Polygon Sum of all the sides Regular Polygon 2nR sin (180°/n), where n is the number of sides and R is the circumradius (distance from the center to one of the vertices of the polygon)

## How to Find Perimeter

There are different ways to find the perimeter of a given shape apart from the formulas given above. We can use a ruler to measure the length of the sides of a small regular shape such as square, rectangle, parallelogram, etc. The perimeter will be obtained by adding the measurements of the sides/edges of the shape.

We can use a string or thread for small irregular shapes. In this case, place either a string or thread precisely along the figure’s boundary once. The total length of the string used along the border of the shape is its perimeter.

### Perimeter Units

Units are essential while representing the parameters of any geometric figure. For example, the length of a line segment measured is 10 cm or 10 m, here cm and m represent the units of measurement of the length. Similarly, the units for perimeter are the same as for the length of the sides or given parameter. If the length of the side of a square is given cm, then the units for perimeter will be in cm. There is another case, where the dimensions are given in two different units such as length of a rectangle in ft and breadth in inches, then units for the perimeter of a rectangle will be ft, for this we need to convert both the measurements into ft.

We will solve here some of the example questions to understand how to find the perimeter of different shapes.

### Examples

Question.1: What is the perimeter of an equilateral triangle whose side length is 7 cm?

Solution: Given, length of the side of equilateral triangle is 7 cm

As we know, the equilateral triangle has all its sides equal in length.

Therefore,

Perimeter of triangle = a+b+c

Here,

a = b = c

Therefore,

Perimeter = 3a

P = 3 x 7 = 21 cm

Question 2: If the length of parallel sides of a parallelogram is 8 cm and 11 cm, respectively, then find its perimeter.

Solution:

Given,

Length of parallel sides of a parallelogram is 8 cm and 11 cm, respectively.

By the formula of perimeter, we know;

Perimeter of Parallelogram = 2(a+b)

P = 2 (8 + 11)

P = 2 x 19

P = 38 cm

Therefore, the perimeter of a given parallelogram is 38 cm.

Question 3: If the radius of a circle is 21 cm, then find its perimeter.

Solution: Given,

Radius of circle = 21 cm

We know,

Perimeter of circle = Circumference of circle = 2πr

Therefore,

Circumference = 2 × 22/7 × 21

= 2 × 22 × 3

= 132 cm

Therefore, the perimeter of circle here is equal to 21 cm.

Question 4: A regular pentagon of side 3 cm is given. Find its perimeter.

Solution: Given, length of the side of regular pentagon = 3 cm

As we know, a regular pentagon will have all its 5 sides equal.

Hence,

Perimeter of regular pentagon = 5a, where a is the side length

Perimeter = 5 × 3

= 15 cm

Therefore, the answer is 15 cm here.