Circumference and area of a circle · Usually met around P6
Areas of semicircles, rings and shapes made with them
Find the radius first: 3.14 × r × r.
How to do it
Method
Find the radius first: 3.14 × r × r
Semicircle (diameter 8): 3.14 × 4 × 4 ÷ 2 = 25.12
Another way
1.57 × r × r
1.57 × 4 × 4 = 25.12
In full
A circle's area = 3.14 × radius × radius: cut a circle into many thin slices and lay them out as an almost-rectangle, half the circumference (3.14 × radius) long and a radius wide, so the area is 3.14 × radius × radius. Find the radius first: from a diameter, halve it. A semicircle's area is half a circle's; a quarter circle's a quarter. A ring = big circle − small circle = 3.14 × (big radius × big radius − small radius × small radius), not 3.14 × (big − small) × (big − small). For a shape made of pieces, add the pieces, or take the cut-out part away from a bigger shape. A semicircle 8 cm across: 3.14 × 4 × 4 = 50.24, 50.24 ÷ 2 = 25.12 cm²; another way: 1.57 × 4 × 4 = 25.12.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Find the area of this semicircle. (Take π as 3.14.) The answer is □ cm²
Show the answer and working
Answer: 6.28
The radius is 4 ÷ 2 = 2; the circle is 3.14 × 2 × 2 = 12.56, half of it 6.28.
Example 2
The shape is a rectangle and a semicircle. Find its area. (Take π as 3.14.) The answer is □ cm²
Show the answer and working
Answer: 54.28
Rectangle 12 × 4 = 48; semicircle of radius 2: 3.14 × 2 × 2 ÷ 2 = 6.28; 48 + 6.28 = 54.28.
Example 3
A semicircle with a diameter of 24 cm has an area of 226.08 cm². (Take π as 3.14.)
True or false?
Show the answer and working
Answer: True
Use the radius 12, not the diameter: 3.14 × 12 × 12 ÷ 2 = 226.08.
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