Perimeter of Shapes

How to find the perimeter of polygons, compound shapes, and circles using the correct formulas.

What is Perimeter?

The perimeter is the total distance around the outside of a shape. It is measured in length units (cm, m, km).

Perimeter of Common Shapes

Shape	Formula
Square (side $a$ )	$P = 4a$
Rectangle ( $a \times b$ )	$P = 2(a + b)$
Triangle (sides $a, b, c$ )	$P = a + b + c$
Circle (radius $r$ )	$C = 2\pi r$

Compound Shapes

For compound shapes (made from simpler shapes), add the lengths of all outer edges only.

An L-shaped room

$P = 10 + 6 + 4 + 8 + 6 + 14 = 48 \text{ cm}$

(Add all six outer edges)

Circumference of a Circle

A circle with radius 5 cm

$C = 2\pi r = 2 \times 3.14 \times 5 = 31.4 \text{ cm}$

Or using diameter $d = 10$ : $C = \pi d = 31.4 \text{ cm}$

Note

Circumference = perimeter of a circle. Remember: $d = 2r$ .

Real world: fencing a garden

A rectangular garden is 12 m long and 8 m wide. The owner wants to fence all four sides. $P = 2(12 + 8) = 40\text{ m}$ of fencing is needed. If fence panels are 2 m wide, they need $40 \div 2 = 20$ panels. Perimeter directly determines material costs.

Real world: a running track

A circular running track has a radius of 40 m. One full lap $= C = 2\pi \times 40 \approx 251\text{ m}$ . Knowing the circumference, athletes can calculate how many laps are needed to run 1500 m: $1500 \div 251 \approx 6$ laps.

Real world: framing a picture

A painting measures 60 cm × 40 cm. A framer needs to cut a length of moulding equal to the perimeter: $P = 2(60 + 40) = 200\text{ cm} = 2\text{ m}$ . Perimeter calculations prevent buying too much or too little frame material.

Tip Perimeter is always measured in the same unit as the side lengths. If sides are in cm, perimeter is in cm — never cm².

Practice Problems

Find the perimeter of a rectangle with length 9 cm and width 5 cm.

Show answer

P = 2(9 + 5) = 28 cm.

A circle has a diameter of 14 cm. Find its circumference (use π ≈ 3.14).

Show answer

C = π × 14 = 43.96 cm.

A square has a perimeter of 36 cm. What is its side length?

Show answer

a = 36 ÷ 4 = 9 cm.