Shape and Space (Composite shapes)

When calculating an area, you may not always be faced with regular shapes.  In some instances you may need to break a more complicated shape down into a series of simpler shapes, which are easier to deal with.

Example

You plan to lay turf down for your new garden. In order to calculate how much turf to buy you need to first work out the surface area.  The dimensions of the garden are shown below.

Answer

In order to calculate the Area of the garden you must first break the garden up into 3 simple shape.  One long rectangle across the top, one square and one triangle, as seen below.

The area of the rectangle = 4 x 8 = 32m²
The area of the square = 4 x 4 = 16m²
The area of the triangle = 1/2 4 x 4 = 8m²

Therefore the area of the garden = 32 + 16 + 8 = 56 m²