Perimeter of square and rectangle

The perimeter of a square or rectangle is the total length of the path around the figure – if you wanted to wrap a string around it, the string would be that long.

Perimeter of a square

A square has four sides of the same length. Let's call that length side a.

If a square has a side of 5 cm, you can compute the perimeter in two ways:

5 + 5 + 5 + 5 = 20 cm (add all four sides)
4 · 5 = 20 cm (multiply one side by four)

The formula:

P = 4 · a

In words: the perimeter of a square is four times the side.

Worked example

A square has a side of 8 m. What is the perimeter?

Solution: P = 4 · 8 = 32 m. The perimeter of the square is 32 meters.

Perimeter of a rectangle

A rectangle has two longer sides and two shorter sides. Let's call the longer side a and the shorter side b. Opposite sides are equal in length.

If a rectangle has sides 6 cm and 4 cm, the perimeter is:

6 + 4 + 6 + 4 = 20 cm (add all four sides)
2 · (6 + 4) = 2 · 10 = 20 cm (add the long and short side, then multiply by two)

The formula:

P = 2 · (a + b)

In words: the perimeter of a rectangle is twice the sum of the longer and shorter sides.

Worked example

A rectangle has sides 12 cm and 5 cm. What is the perimeter?

Solution: P = 2 · (12 + 5) = 2 · 17 = 34 cm. The perimeter is 34 centimeters.

Common mistakes

Most common mistakes with the rectangle formula:

Adding only the longer and shorter side – the result is half of the real perimeter. You still need to multiply by two (or add all four sides).
Forgetting the parentheses: computing 2 · a first and then adding b. That is wrong – the parentheses tell you to add first, then multiply.

When a rectangle is actually a square

A square is a special rectangle – one where the longer and shorter sides happen to be equal. So the rectangle formula always works for a square too: 2 · (a + a) = 4 · a. Same answer.

Practice

Try the generator – it picks a square or rectangle at random, and the sides and units change every time.

Generator: Perimeter of square and rectangle