Area and Perimeter of a Square

Formulas for the area, perimeter, and diagonal of a square, with worked examples.

Square

A square is a rectangle where all four sides are equal. All angles are 90°.

Area of a Square

A = a^2

Area is the side length squared.

Perimeter of a Square

P = 4a

Perimeter is four times the side length.

Diagonal of a Square

d = a\sqrt{2}

The diagonal connects two opposite corners.

Find the area and perimeter of a square with side 5 cm

$A = 5^2 = 25 \text{ cm}^2$

$P = 4 \times 5 = 20 \text{ cm}$

$d = 5\sqrt{2} \approx 7.07 \text{ cm}$

Find the side of a square with area 64 m²

$a = \sqrt{64} = 8 \text{ m}$

Real world: kitchen tiles

Square tiles with side 20 cm are used to tile a floor. Each tile covers $0.2 \times 0.2 = 0.04 \text{ m}^2$ . Dividing the total floor area by 0.04 gives the number of tiles needed.

Real world: square field

A square field has a perimeter of 360 m. Each side is $360 \div 4 = 90 \text{ m}$ , and the area is $90^2 = 8100 \text{ m}^2$ .

Tip

Where do we see squares? Floor tiles, chessboards, sticky notes, window panes, and city blocks are often square. A square is just a special rectangle — all rectangle formulas work for squares too.

Practice Problems

A square has side 9 m. Find its area and perimeter.

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A = 81 m², P = 36 m

A square has area 144 cm². What is its perimeter?

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Side = √144 = 12 cm. P = 4 × 12 = 48 cm

A square garden has perimeter 52 m. Find its area.

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Side = 52 ÷ 4 = 13 m. A = 13² = 169 m²