Area of irregular shapes

In a nutshell

Sometimes you will need to work out the area of odd shapes you may not have come across before. You can use what you already know to learn how to work out the area of these irregular shapes.

Finding the area of an irregular shape

The area of an unknown shape will be made up of different, smaller shapes, put together. In this instance, you will need to work out the area for all the smaller shapes then add them all up.

Example 1

Find the area of the following shape, given that the length of each square is $$1cm$$​.

Firstly, find the smaller shapes you are familiar with which make up this irregular shape.

You can see that the bottom half of the shape is a rectangle and the top corners are in the shape of a triangle. 

Find the area of the rectangle.

​$$Area = l \times w \\length = 4cm, \ width = 2cm \\Area = 4 \times 2 = \underline{8cm^2}$$​​

Next, find the area of the triangles.

$$Area = \frac{1}{2} \times \ b \times h \\base = 2cm, \ height = 2cm \\Area = \frac{1}{2} \times \ 2 \times 2 \ = \underline{2cm^2}$$​​

As there are two triangles you will need to multiply the area found for one of the triangles by two.

​$$Area \ for \ two \ triangles = 2 \times2 = \underline{4cm^2}$$​​

Now find the total area of the irregular shape by adding the areas of the rectangles and both triangles.

​$$The \ total \ area \ of \ the \ shape = 8 \ + 4 = \underline{12cm^2}$$.

Note: You can also find the area by counting the squares.

Example 2

Find the area of the following shape by counting the squares.

Firstly, count the number of squares in the shape. If you take a closer look, you will see that this shape is made up of $$10$$​ full squares and $$4$$​ half squares. The $$4$$ half squares equal to $$2$$ full squares. The total number of full squares is $$12.$$

Find the area of the shape if each square is $$1cm^2$$.

$$The \ total \ area \ of \ the \ shape \ is \ \underline{12cm^2}$$.