Perimeter Formulas

Perimeter:  The perimeter is the total distance around the outside of a two- dimensional shape. You calculate it by adding together all the length of a shape.  In any polygon, the perimeter can be calculated by adding all the lengths of the sides. The perimeter of any polygon is the sum of the lengths of all the sides.

Square: In a square since all the sides are same, the formula for finding a perimeter of a square = 4 x side, where side is represented by a. Alternatively, we can add all the four sides to find the perimeter: a+a+a+a = 4a

Perimeter of a square = 4a

Rectangle:  In a rectangle as we know the length and width are different, the perimeter of a rectangle is 2 x (l+b) where l refers to the length and b stands for width of a rectangle. In the given diagram the length is a and b stands for width.

Perimeter of a rectangle = 2a + 2b

Triangles: The triangles are three sided geometrical closed figures. The perimeter of a triangle can be obtained by adding all the sides i.e, the formula for finding the perimeter of a triangle is a+b+c

Perimeter of a triangle = a + b + c   

Circle: The perimeter of a circle is called its circumference. The ratio of the circumference of a circle to its diameter is a constant, which is universally denoted by pi (). Therefore the circumference or perimeter of a circle : 2r or d where r stands for the radius and d stands for the diameter of a circle.  An approximate value of  is 22/7 which is correct to two decimal places. A more accurate value of  is 3.1416 which is correct to four decimal places.

Perimeter of a circle= 2 r   (where r is the radius) or
=  d (where d is the diameter)

Note:  All the units must be same while calculating the perimeter. For example, if the question is:

The length of a rectangle measures 1 ft and the width of the rectangle measures 6 inches. What is the perimeter of a rectangle?

First, we need to have the same units of measurement.  Therefore, we must convert the ft into inches or inches into ft.  As, we know 1 ft = 12 inches.  Converting the width of a rectangle that is 6 inches into feet would = 6/12. After simplification we get ½ or 0.5 ft.

Perimeter = 2 (length + width)
=2(1+0.5)
=2(1.5 ft)
=3 ft