Area calculator for 2D shapes with working

• Rectangle: 8 cm by 5 cm. $8 \times 5 = 40$ cm².
• Triangle: base 10 cm, height 6 cm. $\tfrac{1}{2} \times 10 \times 6 = 30$ cm².
• Trapezium: parallel sides 4 cm and 10 cm, height 5 cm. $\tfrac{1}{2} \times (4 + 10) \times 5 = 35$ cm².
• Circle: radius 3 cm. $\pi \times 3^2 = 9\pi \approx 28.27$ cm².

For triangles, parallelograms and trapeziums, the height must be perpendicular (at right angles) to the base, not the length of a sloping side. A parallelogram with a base of 8 cm, sloping sides of 5 cm and a perpendicular height of 4 cm has an area of $8 \times 4 = 32$ cm², not $8 \times 5$.

Split an L-shape or an irregular shape into rectangles, triangles and other simple shapes, find each area, then add them (or subtract a cut-out piece). Label each part on the diagram so you don't count any piece twice, and check the missing lengths by subtracting from the given totals.

Area is measured in square units. Converting needs the square of the length conversion: $1 \text{ m}^2 = 100 \times 100 = 10000$ cm², and $1 \text{ cm}^2 = 100$ mm². A common slip is dividing cm² by 100 to get m². For a circle in terms of $\pi$, leave the answer as, for example, $9\pi$ cm² if the question asks for an exact value.

• Using a slant height instead of the perpendicular height.
• Forgetting the $\tfrac{1}{2}$ for triangles and trapeziums.
• Using the diameter in $\pi r^2$: halve it first.
• Mixing units, such as one side in m and another in cm.

Practise with our area and perimeter questions, and see the circle calculator for circumference too.

• Write the formula, then substitute: method marks are often given even if the arithmetic slips.
• On non-calculator papers, leave circle answers in terms of $\pi$ unless told otherwise.
• Give units, and round only at the end (to 3 significant figures if the question doesn't say).
• Sketch and label the shape if the question only describes it in words.