Perimeter

Perimeter

The distance around the outside of a plane figure. For a polygon, the perimeter is the sum of the lengths of the sides.

See also

Key Formula

P = s_1 + s_2 + s_3 + \cdots + s_n

Where:

$P$ = Perimeter of the polygon
$s_1, s_2, \ldots, s_n$ = Lengths of each side of the polygon
$n$ = Number of sides

Worked Example

Problem: Find the perimeter of a rectangle with a length of 12 cm and a width of 5 cm.

Step 1: Identify all side lengths. A rectangle has two pairs of equal sides: two sides of 12 cm and two sides of 5 cm.

Step 2: Add all four side lengths together.

P = 12 + 5 + 12 + 5

Step 3: Compute the sum.

P = 34 \text{ cm}

Answer: The perimeter of the rectangle is 34 cm.

Another Example

Problem: Find the perimeter of a triangle with sides measuring 7 m, 10 m, and 13 m.

Step 1: List all side lengths: 7 m, 10 m, and 13 m.

Step 2: Add the three side lengths.

P = 7 + 10 + 13

Step 3: Compute the sum.

P = 30 \text{ m}

Answer: The perimeter of the triangle is 30 m.

Frequently Asked Questions

What is the difference between perimeter and area?

Perimeter measures the distance around the outside of a shape and is expressed in linear units (cm, m, ft). Area measures the amount of surface a shape covers and is expressed in square units (cm², m², ft²). Two shapes can have the same perimeter but very different areas, and vice versa.

How do you find the perimeter of a circle?

The perimeter of a circle is called its circumference. You calculate it with the formula

C = 2\pi r

, where

r

is the radius, or equivalently

C = \pi d

, where

d

is the diameter.

Perimeter vs. Area

Perimeter is the total length around the boundary of a shape, measured in linear units like meters or feet. Area is the amount of two-dimensional space enclosed inside the shape, measured in square units like m² or ft². For example, a rectangle that is 6 m by 4 m has a perimeter of 20 m but an area of 24 m². Perimeter answers 'how far around?' while area answers 'how much surface?'

Why It Matters

Perimeter shows up whenever you need to measure or enclose a boundary. Fencing a yard, framing a picture, running a lap around a track, or wrapping ribbon around a gift box all require you to calculate perimeter. Understanding perimeter also lays the groundwork for more advanced geometry topics like circumference, surface area, and optimization problems.

Common Mistakes

Mistake: Confusing perimeter with area and writing the answer in square units.

Correction: Perimeter is a length, so it is always in linear units (cm, m, ft), not square units. If your answer has cm² or m², you likely calculated area instead.

Mistake: Forgetting to include all sides, especially the unlabeled ones in a rectangle or irregular polygon.

Correction: Make sure you count every side. A rectangle has four sides, not two. If a diagram only labels the length and width, remember there is a second copy of each.

Related Terms

Circumference — Perimeter of a circle specifically
Area — Measures enclosed surface, not boundary length
Polygon — Closed plane figure whose perimeter is the side sum
Plane Figure — Any flat shape that has a perimeter
Side of a Polygon — Each segment added to compute perimeter
Sum — Perimeter is the sum of side lengths
Rectangle — Common shape with perimeter formula 2l + 2w