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Perimeter

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What is the Perimeter?

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The word perimeter is introduced from two Greek words 'peri' which defines around and 'metron'; which defines measure. In Geometry, the perimeter of a two-dimensional shape is defined as the path or boundary that encloses the shape. if the given figure is a polygon such as a triangle, square, rectangle, etc, then the perimeter is the sum of the length of all the sides of a polygon. For example, a triangle with side length 4 cm has a perimeter 4 + 4 + 4 = 12.

Some geometrical shapes do not have a finite number of sides, so calculating the perimeter of such shapes is a bit uncomplicated. For example, the perimeter of a circle is stated as the circumference of a circle which can be calculated by using formula 2r, where r is the radius of the circle and the value is 3.14. Let us learn the formulas to calculate the perimeter of different two-dimensional shapes.


Perimeter Formulas of Two-Dimensional Shapes

Let us know learn the perimeter formulas of different two-dimensional shapes:

Perimeter of a Square

The perimeter of a square is the sum of the length of all its four sides. As we know, all the sides of a square are equal, hence the perimeter of a square will be 4 times its side i.e  4 × side.

The perimeter of a Square Formula (P) -  4 × Sides.


Perimeter of a Triangle

The perimeter of a triangle is the sum of the length of all its three sides. For example, if x, y, and z  are the three sides of a triangle, then the perimeter of that triangle will be x + y + z.


Triangle


The perimeter of a Triangle Formulas (P) - Sum of the length of all its three sides.


Perimeter of Equilateral Triangle

The equilateral triangle is the triangle where all the sides and angles are equal. Hence, the perimeter of the equilateral triangle will be calculated by using the formula 3a, where ‘a’ is the side of the triangle.

The perimeter of Equilateral Triangle Formula  (P) = 3a or 3 × side.


Perimeter of Rhombus

The rhombus is often known as a diamond or diamond-shaped object. The total distance traveled along the boundary is termed the perimeter of a rhombus.

The perimeter of a Rhombus Formula (P) =  4a,

In the above perimeter of a rhombus formula, the variable ‘a’  is the length of the side of the rhombus.


Perimeter of Cube

The perimeter of a cube relies on the number of edges it has and the length of the edges of a cube. As the cube has 12 edges and all the edges are similar in length. Therefore the perimeter of a cube is calculated by using the formula 12l.

The perimeter of Cube Formula (P) =  12l

Where l is stated as the length of the edge of the cube.


Perimeter of Rectangle

The perimeter of a rectangle is defined as the sum of the length of all its 4 sides. As we know, opposite sides of a rectangle are equal, and accordingly, the perimeter of a rectangle will be twice the length of a rectangle plus twice the breadth of the rectangle and it is represented by the alphabet p.

The perimeter of a Rectangle Formula (P) =  2(L + B)units.


Perimeter of Circle

The perimeter of a circle is the measurement of the boundary of a circle. The perimeter of a circle is also defined as the circumference of a circle. The perimeter or circumference of a circle can be calculated using the formulas given below.


Perimeter of Circle Formula

If the radius of a circle is given, the perimeter or circumference of a circle will be calculated by using the formula 2πr, where r is the radius of the circle and the value of is 3.142 approx. 

If the diameter of a circle is given, the perimeter or circumference of a circle will be calculated by using the formula πd, where d is the diameter of the circle and the value of π is 3.142 approx.


Perimeter of Semicircle

A semicircle is a half-circle that is obtained either by dividing the whole circle into two halves or by dividing the circumference of a circle by 2. The perimeter of a semicircle is half of the circumference of an original circle C, plus the diameter d. The perimeter of the semicircle can be calculated by using the formula given below.


Semicircle


Perimeter of Semicircle Formula (P) =  ½ (2πr) + d, or  P = πr + d.

In the above perimeter of the semicircle formula, variables ‘d‘ and ‘r’ are the diameter and the radius of a circle respectively.


Perimeter of Parallelogram

A parallelogram is a two-dimensional geometric shape enclosed by its four sides. The perimeter of a parallelogram is the sum of all the lengths of all its four sides. We know the opposite sides of a parallelogram are equal and parallel to each other. Accordingly, the perimeter of a parallelogram is calculated by using the formula given below.

Perimeter of Parallelogram Formula (P) = 2(a + b) units.


Solved Examples

1. Calculate the perimeter of a square, if the length of the sides of a square is 10cm.

Solution: As we know, the perimeter of a square is 4 × side

Accordingly, the perimeter of a square will be 4 × 10 = 40 cm.

Hence, the perimeter of a given square is 40 cm.


2. The length and breadth of a rectangular garden is 150 m and 110 m respectively. Find the perimeter of a rectangular garden.

Solution: As we know, the perimeter of a rectangle is 2( length + breadth).

Accordingly, the perimeter of a rectangular garden is 2(150 + 110) = 2(260) = 520 meters.

Hence, the perimeter of a rectangular garden is 44 meters.


3. Find the perimeter of an equilateral triangle whose side is 8 cm

Solution: As we know, the perimeter of an equilateral triangle is 3 × side.

Accordingly, the perimeter of an equilateral triangle is 3 × 8 = 24 cm.

Hence, the perimeter of a given equilateral triangle is 24 cm.


Fun Facts

  • Different rectangles with similar perimeter can have different areas.

  • The perimeter of the square and rectangle is always smaller than their area whereas the perimeter of the triangle can be more than its area.

FAQ (Frequently Asked Questions)

1. How Units are Important in Perimeter?

Ans: Units play an important role while representing the perimeter of any two-dimensional geometrical figure. For example, if the measurement of the length of all the sides of the two-dimensional figure is given in cm, then the unit of the measurement of a perimeter will be the same i.e. in cm.


In another case, if the dimensions of a rectangle are given in two units such as the length of a rectangle is given in inches and the breadth of the rectangle is given in inches, then the unit for the perimeter of a rectangle will be in feet. In this case, we will convert both the measurement into one unit i.e. in feet.

2. How to Calculate the Perimeter of a Two-Dimensional Figure?

Ans: There are different ways to calculate the perimeter of a two- dimensional figure apart from the formulas discussed above are given below:

  • We can use the ruler to measure the length of the sides of a regular polygon such as square, rectangle, etc.

  • The perimeter can also be calculated by adding the length of all the sides/edges of a given figure. We can even use a small thread or string to calculate the perimeter of a given shape.

  • The total length of a thread or string used along the boundary of a shape is considered as its perimeter.