Geometry

Areas of Shapes

Areas of Shapes

Area is the amount of space taken up in 2 dimensions. The units of area are generally mm2, cm2, m2, and km2. We must be careful changing from one unit to another, for example:

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1m2 = 100cm x 100cm

1m2 = 10000cm2

Area of a Rectangle

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A = b x h

A = 7 x 6

A = 42m2

Sometimes we are given the area of a rectangle and are required to find a dimension. For example:

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A = b x h

84 = 12 x h

(12) (12)

h = 7m

Area of a Triangle

Strategy: We consider a triangle as an ‘encased’ rectangle with half its area removed.

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A = (base x height) 2

A = (25 x 12) 2

A = 300 2

A = 150m2

Example 2: A triangle has an area of 120m2 and a base length of 10m. Find it’s vertical height.

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A = (b x h) 2

120 = (10 x h) 2

(Multiply each side by 2)

240 = 10 x h

( 10) (10)

h = 24m

Area of a Parallelogram

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This is straightforward because a parallelogram is a quadrilateral with two pairs of parallel sides – it can be seen as a rectangle that has been pushed to one side.

A = b x h

Area of a Trapezium

A =