---
title: "Area: cheat sheet"
subtitle: "Area, volume, circles and Pythagoras"
---

# Area

> The words and methods from this unit, with an example of each.

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**perpendicular height**: The distance from the base to the opposite side or corner, at a right angle (∟) to the base. A slanted side is longer, and is not the height.

$$h \text{ at } 90^\circ \text{ to } b$$

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**area of a parallelogram**: Cut the triangle off one end and move it: a rectangle with the same base and height.

$$A = b \times h$$

_A parallelogram cut and rearranged into a 6 by 4 rectangle_

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**area of a triangle**: Two copies make a parallelogram with the same base and height; the triangle is half.

$$A = \tfrac{1}{2} \times b \times h$$

_A triangle and its turned copy make a parallelogram_

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**composite area**: Split the shape into rectangles and triangles and add the parts, or subtract a missing part from a bigger shape. Put every length in the same unit first.

$$24 + 9 = 33 \text{ m}^2$$

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**square units**: Area counts squares: cm², m². A 1 m square is 100 cm by 100 cm.

$$1 \text{ m}^2 = 10\,000 \text{ cm}^2$$

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**composite area**: Cut the shape into pieces you know and add their areas, or take the missing pieces away from a big rectangle. Each piece uses its own lengths.

$$A = 8 \times 6 - 5 \times 3 = 33\ \text{m}^2$$

_An L-shape with its side lengths_

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**estimating an irregular area**: Count the full squares, add half the part squares, multiply by the area of one square. A finer grid gives a closer estimate.

$$A \approx (\text{full} + \tfrac{1}{2} \times \text{part}) \times \text{one square}$$

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