Area of Rectangles and Triangles

In a Nutshell

Area measures the amount of space inside a 2D shape. For a rectangle, multiply length by width. For a triangle, halve the base times the height.

Area of a rectangle

Area is measured in square units such as cm2\text{cm}^2, m2\text{m}^2 or mm2\text{mm}^2. For a rectangle the formula is:

Area=length×width\text{Area} = \text{length} \times \text{width}

Think of filling the rectangle with unit squares. A rectangle that is 5 cm long and 3 cm wide holds 5×3=155 \times 3 = 15 unit squares, so its area is 15 cm215 \, \text{cm}^2.

Area of a triangle

Every triangle is exactly half of a rectangle (or parallelogram) with the same base and height. So:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

The height must be perpendicular to the base — the vertical distance, not a slanted side.

Explore: rectangle

Area of a rectangle An interactive diagram showing the area of a rectangle on a square grid. b h

Change the base and height, then press Update to see the area recalculated on the grid.

Explore: triangle

Area of a triangle An interactive diagram showing the area of a triangle on a square grid. b h

Watch it work

Question: Find the area of a triangle with base 8 cm8 \, \text{cm} and height 5 cm5 \, \text{cm}.

Have a go

Q1. Find the area of a rectangle with length 7 cm7 \, \text{cm} and width 4 cm4 \, \text{cm}.

Q2. Find the area of a triangle with base 10 cm10 \, \text{cm} and height 6 cm6 \, \text{cm}.

Q3. A rectangular garden is 12 m12 \, \text{m} long and 8 m8 \, \text{m} wide. What is its area?

Q4. A right-angled triangle has legs of 9 cm9 \, \text{cm} and 4 cm4 \, \text{cm}. Find its area.

Q5. The area of a rectangle is 60 cm260 \, \text{cm}^2 and its length is 10 cm10 \, \text{cm}. What is its width?