Perimeter Formulas

The perimeter is the total length all the way around the outside of a shape.

P = 4s P = 2(l + w) P = a + b + c

Perimeter is the distance around the outside. This 5-by-3 rectangle has perimeter 16.

What each symbol means

Perimeter is the distance all the way around the edge of a flat shape. If you walked around the outside of a field and measured how far you went, that total is the perimeter. You can always find it by adding up every side, but for common shapes there are quick formulas.

The three you need most

Square

A square has four equal sides, so the perimeter is P = 4s. Just multiply one side by 4. For example, a square with sides of 5 cm has a perimeter of 4 × 5 = 20 cm.

Rectangle

A rectangle has two long sides and two short sides, so the perimeter is P = 2(l + w). Add the length and width, then double it. For example, a rectangle 6 cm by 4 cm has a perimeter of 2 × (6 + 4) = 2 × 10 = 20 cm.

Triangle

A triangle has three sides, so the perimeter is just P = a + b + c. Add all three side lengths. For example, a triangle with sides 3, 4, and 5 has a perimeter of 3 + 4 + 5 = 12.

Perimeter uses plain units: Perimeter is a length, so it is measured in plain units like cm or m - never square units. Square units are for area, which measures the space inside instead.

A worked example

Find the perimeter of a rectangle 12 m long and 5 m wide

  1. Use the rectangle formula: P = 2(l + w).
  2. Put in the numbers: P = 2(12 + 5).
  3. Add the length and width first: 12 + 5 = 17.
  4. Double it: 2 × 17 = 34.
  5. The perimeter is 34 meters.

Why these formulas work (they are just shortcuts for adding)

  1. Perimeter always means "add up every side". The formulas are just faster ways to do that adding.
  2. A square has four sides all the same length s, so s + s + s + s = 4s. Multiplying by 4 is quicker than adding four times.
  3. A rectangle has two sides of length l and two of width w, so the total is l + w + l + w = 2l + 2w = 2(l + w).
  4. A triangle has three sides that can all be different, so there is no shortcut: you simply add them, a + b + c.
  5. Every perimeter formula is just the sum of the sides, written in the shortest way for that shape.

Practice questions

Question 1

Find the perimeter of a square with side 9 cm.

  1. A square has four equal sides, so use P = 4s.
  2. Substitute the side length s = 9: P = 4 × 9.
  3. Multiply: P = 36.
  4. The perimeter is 36 cm (a plain length unit).

Answer: 36 cm

Question 2

Find the perimeter of a rectangle 8 m long and 3 m wide.

  1. A rectangle uses P = 2(l + w).
  2. Substitute l = 8 and w = 3: P = 2(8 + 3).
  3. Add the length and width: 8 + 3 = 11.
  4. Double it: 2 × 11 = 22 m.

Answer: 22 m

Question 3

A triangle has sides 7 cm, 10 cm, and 5 cm. What is its perimeter?

  1. A triangle uses P = a + b + c.
  2. Substitute the three sides: P = 7 + 10 + 5.
  3. Add them step by step: 7 + 10 = 17, then 17 + 5 = 22.
  4. The perimeter is 22 cm.

Answer: 22 cm

Question 4

A square field has a perimeter of 40 m. How long is each side?

  1. Start from P = 4s with P = 40.
  2. This gives 40 = 4 × s.
  3. To find one side, divide the perimeter by 4: s = 40 ÷ 4.
  4. Work it out: s = 10 m.

Answer: 10 m

Question 5

A rectangle has a perimeter of 30 cm and a width of 5 cm. Find its length.

  1. Start from P = 2(l + w) with P = 30 and w = 5.
  2. This gives 30 = 2(l + 5). Divide both sides by 2: 15 = l + 5.
  3. Subtract the width: l = 15 - 5.
  4. Work it out: l = 10 cm.

Answer: 10 cm