# Areas of Basic Shapes

A number of expressions are available to calculate the area of a region defined by a basic shape, as shown in the illustration above, and summarised in the table below.

Shape | Area | Shape | Area | Shape | Area |
---|---|---|---|---|---|

Square | Trapezoid | Ellipse | |||

Rectangle / Parallelogram |
Triangle | Circle |

The basic approach is to:

- Identify the shape, and the appropriatete equation.
- Find all required parameters (width, height, radius, etc.).
- Convert all lengths to the chosen unit, if necessary.
- Calculate the area and remember to add the appropriate unit of area (unit
^{2}).

#### Worked Example 1

Find the area of a triangle with a base width of 1.4 m and a height perpendicular to the base of 0.4 m. Give your answer in square metres.

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b = 1.4 m and h = 0.4 m

A = 1 / 2 × b × h

= 0.5 × 1.4 × 0.4

= 0.28 m^{2}

#### Worked Example 2

Find the area of a circle of radius 4 cm. Give your answer in cm^{2}.

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A = π × r^{2}

= π × 4^{2}

= 50.27 cm^{2} to 2 d.p.

#### Worked Example 3

Find the area of a rectangle with a base of 80 cm and a height of 50 cm. Give your answer in m^{2}.

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The answer needs to be in m^{2} so begin by converting all lengths to metres.

b = 0.8 m, h = 0.5 m

A = b × h

= 0.8 × 0.5

= 0.4 m^{2}