Compound Shapes: How to Find the Area of an L-Shape

A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps:

Step 1: Work out the missing lengths around the edge of the compound shape.

Step 2: Divide your L shape into two rectangles. This can be done in 2 different ways (both methods will give the same answer).

Step 3: Work out the area of each rectangle. Do this by multiplying the base of the rectangle by the height of the rectangle.

Step 4: Add the areas of the rectangles together to give the total area of the L shape.

Example 1

Find the area of this compound shape (L shape).

Step 1

Work out the missing lengths around the edge of the compound shape.

10 – 6 = 4 cm

9 – 2 = 7 cm

Step 2

Divide your L shape into two rectangles.

In this case I have put the line horizontal.

Step 3

Now you need to find the area of the 2 rectangles:

The area of rectangle A is 10 × 2  = 20 cm²

The area of rectangle B is 4 × 7 = 28 cm²

Make sure you select the correct base and height lengths for each rectangle.

Step 4

All you need to do now is to add up the 2 answers from step 3.

20 + 28 = 48 cm².

So the total area of the compound shape is 48 cm².

Summary:

Find the missing lengths around your L shape and divide the shape into 2 rectangles. Find the area of both rectangle and add them up to give the total area of the compound shape.