Perimeter Formulas 

Perimeter is the path or boundary around a shape or can also be known as the outline of a shape. In geometry, there are different kinds of shapes that we encounter from 2D shapes to 3D shapes. Perimeter formulas cover the formulas of various 2-d shapes in geometry. Let's learn the various formulas of various shapes and solve a few examples as well. 

Meaning of Perimeter Formulas

Perimeter formulas are used to find the distance around the 2-d shape by adding its side lengths. Perimeter is considered as the total length of the sides of different shapes. The perimeter formula can be determined if we know the dimensions of the shape. Every polygon has a different perimeter formula depending on the shape of the object. The image below shows all the formulas for different shapes in geometry.

Perimeter Formula of Different Shapes

The perimeter formula can be defined as the sum of the length of all the sides of any geometric shape. Various shapes in geometry have a perimeter formula depending on the shape and size. Let us look at the perimeter formulas of these shapes. 

Perimeter Formula of a Square 

As we already know, the perimeter is the length of the sides or boundary or path of a shape. The perimeter formula of a square can be calculated by adding the length of all its sides. The formula to calculate the perimeter of a square can be given as,

Perimeter of a Square, (P) = 4 × Side units

Perimeter Formula of a Rectangle 

The perimeter formula of a rectangle depends on the distance covered of the entire rectangle i.e. the boundary or covering all 4 sides of the rectangle. l + b + l + b = 2l + 2b = 2(l+b). The perimeter of a rectangle is equal to twice the sum of its length and breadth. Hence, the formula for the perimeter of a rectangle is:

Perimeter of a Rectangle, (P) = 2(l + b) units

Where, 

• l is the length of the rectangle 
• b is the breadth of the rectangle

Perimeter Formula of a Triangle

The perimeter formula of a triangle can be calculated by adding all the sides, in this case, all the three sides of a triangle. There are different perimeter formulas used for different types of triangles. But the general formula used to find the perimeter of a triangle is: 

Perimeter of a Triangle = Sum of all three sides

The perimeter formulas for different types of triangles are: 

• Perimeter of a Scalene Triangle =  a + b + c, where a, b, and c are the three different sides
• Perimeter of an Isosceles Triangle = 2a + b, where a is the length of each of the two sides of equal length and b is the third side.
• Perimeter of an Equilateral Triangle = 3 × a, where a is the length of each side of the triangle
• Perimeter of a Right Triangle =  p + b + h or p + b + √(p2 + b2), where h is the hypotenuse of a right triangle, p is the perpendicular of a right triangle, and b is the base of a right triangle
• Perimeter of Right Isosceles Triangle =  h + 2l, where h is the height and l is the length

Perimeter Formula of a Parallelogram 

The perimeter formula of a parallelogram is determined by the sum of all the sides that are equal to each other. However, the perimeter formula of a parallelogram can also found if the sides of the object are not mentioned but the diagonals or an angle are mentioned. Therefore, the formula to calculate the perimeter of a parallelogram is:

• Perimeter of a Parallelogram (with sides), P = 2 (a + b), where a and b are the two adjacent sides
• Perimeter of a Parallelogram (with one side and diagonals), P = 2a + √(2x² + 2y² - 4a²), where a is one side and x and y are the diagonals
• Perimeter of a Parallelogram (with side, height, and angle), P = 2a + 2h / sin θ, where a is the side, h is the height, and θ is the angle

Perimeter Formula of a Circle 

The perimeter formula of a circle consists of two main components - 2 constants and one radius of the circle. The formula for the perimeter of a circle is the circumference of the circle and the formula to calculate the perimeter or circumference of a circle is: 

Perimeter of a Circle = 2 π r = π d

Where, 

• r is the radius of the circle
• d is the diameter of the circle 
• π(pi) is approx measured at 3.412

Perimeter Formula of a Rhombus

The perimeter formula of a rhombus is calculated by adding the lengths of all the sides of the shape. There are two parameters in which the formula of a perimeter of a rhombus can be calculated - when the sides are given and when the angles are given. Hence, the formula for the perimeter of a rhombus is: 

• Perimeter of a Rhombus (with sides), P = 4a, where a is the length of the sides 
• Perimeter of a Rhombus (with angles), P =  2√(d1)²+(d2)², where d1 and d2 are the lengths of the diagonals

Perimeter Formula of a Trapezoid 

The formula to calculate the perimeter of a trapezoid is by adding the lengths of all four sides of the object. The perimeter formula of a trapezoid makes sure it covers the complete boundary of a trapezoid. Hence, the formula to calculate the perimeter of a trapezoid is:

Perimeter of a Trapezoid, P = Sum of all sides = a + b + c + d, where a, b, c, and d are the lengths of the sides

Perimeter Formula of a Kite 

The perimeter formula of a kite is calculated by adding all the sides of a kite and the distance is calculated by adding the sides of each pair. Hence, the formula to calculate the perimeter of a kite is: 

Perimeter of a Kite, P = 2(a+b), where a and b are the lengths of the two pairs of kites

Perimeter Formula of Polygons

As polygons are closed plane shapes, thus, the perimeter of the polygons also lies in a two-dimensional plane. The perimeter formula of a polygon can be calculated by measuring the total length of the polygon. The perimeter of polygons is calculated in two ways: with respect to regular polygons and irregular polygons. The formula to calculate the perimeter of a regular polygon is: 

Regular Polygons:

• Perimeter of a Hexagon = 6 × (length of one side)
• Perimeter of a Pentagon = 5 × (length of one side)

Irregular Polygons:

Perimeter of Irregular Polygons = Sum of all sides 

Examples Using Perimeter Formula

Example 1: Josie wants to add some lace as decoration to the borders of her tabletop sheet. The tabletop sheet is in the shape of a rectangle. The length of the tabletop sheet is 140 inches and the breadth is 95 inches. How long will be the lace needed?

Solution: Given, length l = 140 in , breadth b = 95 in

The length of the lace = Perimeter of the sheet

 We know the Perimeter formula of a rectangle = 2(l+b).

Applying the values of length and breadth in this formula we have Perimeter = 2(l+b) = 2 (140 + 95) = 2  × 235 = 470 inches.

Therefore Josie will need 470 inches of lace.

Example 2: Determine the length of the side of the equilateral triangle, if its perimeter is 30 units.

Solution: Given, the perimeter of the equilateral triangle = 30 

Let the length of the side of the equilateral triangle be a.

a is calculated using the perimeter formula of an equilateral triangle.

P = 3 × a
30 = 3 × a

a = 30/3

a = 10 units

Therefore, the length of the side of the equilateral triangle is 10 units.

Example 3: If the perimeter of a square is 74 units, find its side.

Solution: Given: Perimeter of square P = 74 units

Using the perimeter formula of a square, 

P = 4 × side units
74 = 4 × side 

Side = 74/4 

Side = 18.5 units

Therefore, the side of a square is 18.5 units