Math Help for Finding the Perimeter of Plane Shapes

Like area, perimeter is another important parameter for defining a plane geometric shape. In this study guide we will discuss the perimeter of a circle, triangle, rectangle and square.

What is Perimeter?

Perimeter is the total length of the outer boundary of any plane area. The outer boundary of a plane area may be either a smooth curve or connected line segments or a combination of both. Finding the perimeter means calculating the total length of the boundary curve or line segments.

Formulas

• Circle: The perimeter of a circle can be calculated using the following formula:

P = 2 * Π * R…………Eqn.1

Where,

P – Perimeter of the circle.

R – Radius of the circle.

• Triangle: The perimeter of a triangle can be calculated using the following formula:

P = A + B + C ……….Eqn.2

Where,

P is the perimeter of the triangle.

A, B, C are the three sides of the triangle.

For equilateral triangles, Eqn.2 can be modified as:

P = 3 * A……………..Eqn.3

Where,

A is the length of the sides of the triangle.

For isosceles triangles, Eqn.2 can be modified as:

P = (2 * A) + B ……..Eqn.4

Where,

A is the length of the equal sides of the triangle.

B is the unequal side length.

• Rectangle: The following formula is used for finding the perimeter of rectangle:

P = 2 * (A +B)……….Eqn.5

Where,

P is perimeter of the rectangle.

A and B are the length of the two sides of the rectangle.

• Square: A square is a special rectangle, which has equal sides . So, from Eqn.5, we can write formulae for finding perimeter of square as below:

P = 4 * A ……………Eqn.6

Where,

P is the perimeter of the square.

A is the length of the sides.

Units

Finding perimeter means calculating the total length of the boundary curve or line segments, so the units are the same as units of length (i.e., mm, inch, meter etc.)

Practice Problems

1. What is the perimeter of a triangle with a base of 4 mm and two sides of 2 mm and 6 mm?
2. Find the perimeter of an equilateral triangle, whose sides are 10 mm long?
3. Find the area of the rectangle, which has two sides of 10 inches and 5 inches?

Answers

1. 12 mm
2. 30 mm
3. 30 inch

If you’re still fuzzy continue doing practice problems until the concept becomes easier for you. Practicing math problems will help you remember the formulas for finding the perimeter for different plane geometry shapes.