Compound Shapes: How to Find the Area of an LShape
Area Of A Composite Shape Video
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.
Questions & Answers
How do you know which sides to multiply on the L shape?
It must be the length and width of the rectangle (these are the two side lengths which make the rectangle).
Helpful 87How do you work out the volume of a prism from calculating the area of an L shape?
Once you have calculated the crosssectional area of the prism, multiply the answer by the length of the prism.
So for example, if the crosssectional area of the L shape was 50 cm^2 and the length 3cm, then the volume of the L shape would be 150 cm^3 (50 multiplied by 3).
Helpful 63How do you know which measurements you are meant to multiply to find the area of a complex shape?
You multiply the two side lengths of each rectangle together (Base multiplied by Height).
Helpful 43How do you find the area of a frame?
Work out the area of the inner and outer rectangles, and then find the difference between these area.
Assuming that the frame is rectangular.
Helpful 40What if I need to find the area of something that is not Lshaped?
Other shapes can be split into rectangles too. T and H shapes are also common exam questions.
Helpful 10
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