Perimeter

Key Notes :

πŸ’‘ The perimeter of a shape is the distance around the shape. It is the total length of the shape’s sides.

What is the perimeter?

Perimeter is the distance around the outside of a two-dimensional shape. The perimeter of a shape is the total length of the shape’s sides. Perimeter is measured in units such as centimeters, inches, feet, yards, meters, kilometers, and miles.

πŸ“£Calculating Perimeter: To find the perimeter of a polygon, add together the lengths of all its sides

Formulas:

  • Square: Perimeter = 4 Γ— side length
  • Rectangle: Perimeter = 2 Γ— (length + width)
  • Triangle: Perimeter = sum of the lengths of all three sides

Let’s try it!

πŸ”΄ The perimeter of this triangle is highlighted.

Triangle with sides three centimeters, four centimeters, and five centimeters. The sides are highlighted to represent the perimeter.

To find the perimeter, add the lengths of all three sides.

3 + 4 + 5 = 12

So, the perimeter is 12 centimeters!

πŸ”΄ The perimeter of the rectangle is highlighted.

Rectangle with sides two centimeters, five centimeters, two centimeters, and five centimeters. The sides are highlighted to represent the perimeter.

To find the perimeter, add the lengths of all four sides.

2 + 5 + 2 + 5 = 14

So, the perimeter is 14 centimeters!

πŸ”΄ Perimeter formula  for rectangles

You can use multiplication to find the perimeter of rectangles and regular polygons.

To find the perimeter of a rectangle, use this formula, where β„“ is the length of the rectangle and w is the width:

P = (2Γ—β„“) + (2Γ—w)

Let’s try it!

Rectangle with a height of six feet and width of four feet.

P = (2Γ—4) + (2Γ—6)

P = 8 +12

P = 20

So, the perimeter is 20 feet!

πŸ”΄Perimeter formula  for regular polygons

A regular polygon is a shape where all the sides are the same length. To find the perimeter of any regular polygon, use this formula, where n is the number of sides and s is the side length:

P = n Γ— s

Let’s try it!

This shape is a regular octagon. An octagon has 8 sides, so n = 8.

A regular octagon with side lengths of two inches.

P = 8 Γ— 2

P = 16

So, the perimeter is 16 inches!

🧿The perimeter of a circle

The perimeter of a circle has a special name. It’s called the circumference.

To find the circumference of a circle, use this formula, where r is the radius:

C = 2Γ—β€‹πœ‹Γ—r

Let’s try it!

A circle with a radius of four meters.

C = 2 Γ— β€‹πœ‹Γ—4

C = 8Γ—β€‹πœ‹

If we use 3.14 for β€‹πœ‹, the circumference is about 25.12 meters!

Learn with an example

πŸ”΄ What is the perimeter of the rectangle?

πŸ₯ To find the perimeter, find the total length of the shape’s sides.

Add all of the side lengths.

6 + 4 + 6 + 4 = 20

The perimeter of the rectangle is 20 meters. (Metres can be written “m”.)

πŸ”΄ What is the perimeter of the shape?

πŸ₯ To find the perimeter, find the total length of the shape’s sides.

Add all of the side lengths.

1 + 7 + 4 + 3 + 5 = 20

The perimeter of the shape is 20 centimeters. (Centimetres can be written “cm”.)

Let’s practice!πŸ–ŠοΈ