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 95How 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 73How 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 51How 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 46How do you know you have to put the line horizontal not vertical when finding the area of an Lshape?
You can split the compound shape up either way.
Both ways will result in the correct area.
Helpful 22
Comments
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