How to Find the Area of Common Shapes

Area is the amount of flat space inside a shape, measured in square units such as cm² or m². Every common shape has a formula: a rectangle is length × width, a triangle is half base × height, and a circle is $\pi r^2$. The key is to use the perpendicular height, not a slanted side.

Rectangle and square

Example: an 8 cm by 5 cm rectangle has area $8 \times 5 = 40$ cm².

Triangle

A triangle is half of a parallelogram with the same base and height:

Example: base 10 cm, height 4 cm gives $\tfrac{1}{2} \times 10 \times 4 = 20$ cm².

Parallelogram

Cut a triangle off one end and move it to the other: you get a rectangle.

Trapezoid (trapezium)

Average the two parallel sides, then multiply by the height:

Example: parallel sides 6 cm and 10 cm, height 4 cm:

Circle

Example: radius 5 m gives $25\pi \approx 78.54$ m². Keep $\pi$ in the answer for an exact result.

Summary table

Units

If lengths are in cm, the area is in cm². Converting area units needs squaring: $1 \text{ m}^2 = 100 \times 100 = 10\,000 \text{ cm}^2$, not 100 cm².

Compound shapes

Split an L-shape or similar into rectangles and triangles, find each area, then add them (or subtract a cut-out piece).

Common mistakes

• Using the slanted side instead of the perpendicular height.
• Using the diameter in $\pi r^2$: halve it first.
• Forgetting to square the units.

Practice questions

1. A triangle with base 12 m and height 7 m.
2. A circle with diameter 10 cm (exact answer).
3. A trapezoid with parallel sides 3 and 9 and height 5.

Answers: 1) 42 m² 2) $25\pi$ cm² 3) 30

The area calculator covers all these shapes with the right units, and the circle calculator works backwards from an area to the radius. For solids, read volume and surface area formulas.

Frequently asked questions

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