We can think of a composite shape as one that is made from a number of smaller shapes. Many complicated shapes can be made by combining simple shapes like triangles, squares, rectangles, and parallelograms in different ways.
Often of the properties of these simpler shapes can be used to understand the composite shape. For example, knowing the total area of all the smaller shapes is the same as knowing the area of the whole composite shape.
We may not always initially know the length of every edge of a shape, but we can use the given information to work out missing lengths. This can be useful if a missing length is needed to find the area of a composite shape.
There will usually be more than one way to break up a composite shape. Some ways may be easier than others, depending on the information that we start with, and whether it is possible to determine initially unknown information.
Find the area of the figure shown.
Find the total area of the figure shown.
Composite shapes are made of simple shapes. Its area can be find by calculating the total area of the simple shapes the whole shape is composed of.
The examples above have explored how adding areas of simple shapes can help us determine the area of a complicated shape. A similar method involves subtracting the area of constituent shapes, and this is particularly useful for composite shapes that have holes and cutaways.
The remaining area is what we get after having taken away the area of the small triangle from the original sheet. That is, we subtract the area of the small triangle from the area of the larger rectangle, and the result is the area of the composite shape that is the remaining paper.
Find the shaded area in the figure shown.
The area of a composite shape with holes and cutaways can be find by subtracting its cutaway area from its larger area.