Lesson 19: Perimeter

New Concept

The distance around a polygon is the perimeter of the polygon. To find the perimeter of a polygon, we add the lengths of its sides.

What’s next

This is just the foundation for working with shapes. Next, you'll apply this concept through worked examples on various polygons and even find missing side lengths.

Property

The distance around a polygon is the perimeter of the polygon. To find the perimeter of a polygon, we add the lengths of its sides.

Examples

A rectangle 3 cm long and 2 cm wide has a perimeter of $3 + 2 + 3 + 2 = 10 \text{ cm}$.
A quadrilateral with sides measuring 10 ft, 12 ft, 11 ft, and 15 ft has a perimeter of $10 + 12 + 11 + 15 = 48 \text{ ft}$.

Explanation

Imagine you're building a tiny fence around a yard. The perimeter is the total length of fence you'd need! You find it by simply walking around the edge and adding up the length of every single side.

Property

The sides of a regular polygon are equal in length. To find its perimeter, multiply the number of sides ($n$) by the length of one side ($s$): $P = n \times s$.

Examples

A regular hexagon (6 sides) with each side measuring 8 mm has a perimeter of $6 \times 8 \text{ mm} = 48 \text{ mm}$.
A regular octagon (8 sides) with each side measuring 12 inches has a perimeter of $8 \times 12 \text{ inches} = 96 \text{ inches}$.

Explanation

Why add the same number over and over again? For regular polygons, where all sides are identical twins, use this awesome shortcut! Just multiply the number of sides by the length of one side to get the perimeter instantly.