Compound C shapes. How to calculate the perimeter and area of a C shape.
Here you will be shown to work out the area and perimeter of a C shape. A C shape is a compound shape made up of 3 rectangles. Make sure you know how to find the area and perimeter of an L shape before you attempt this lesson on C shapes.
To work out the perimeter of the C shape first you will need to work out the sides that are missing around the C shape. Once this is done add up all of the side lengths to give the perimeter of the C shape.
Finding the area of a C shape is a little harder than working out the perimeter. You will have to divide the C shape into 3 rectangles. This can be done in two ways - but both ways will give you the same answer. The next thing to do is to work out the area of the 3 rectangles that you have created. The area of each rectangle can be calculated by multiplying the two side lengths of each rectangle together. Make sure you choose the correct side lengths for each rectangle. Once the area of each rectangle has been found, find the total area of the C shape by summing up the areas of all 3 rectangles.
Let’s take a look at an example.
Work out the area of this C shape:
Let’s find the perimeter first. There is only one side length that is missing which can be found by subtracting the two 3m lengths from the total height of 12m:
12 – 3 – 3 = 6m
All you need to do now is add up all of the side lengths:
12 + 3 + 7 + 6 + 10 + 3 + 15 + 12 = 68m
To calculate the area of the C shape, divide the C shape into 3 rectangles:
The area of rectangle 1 can be found by multiplying the two side lengths together:
12 × 3 = 36 m²
The width of rectangle 2 is missing, this can be found by working out 15 – 10 = 5 m or 12 – 7 = 5m. So the area of rectangle 2 is:
5 × 6 = 30 m²
Finally, work out the area of rectangle 3 by multiplying the two side lengths together:
15 × 3 = 45 m²
So the total area of the compound C shape is:
36 + 30 + 45 = 111 m².
So the perimeter of the C shape is 68m and the area of the C shape is 111m².
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