Circumference and area of a circle · Usually met around P6
Perimeters of semicircles and shapes made with them
Curves from the circumference, add every straight edge.
How to do it
Method
Curves from the circumference, add every straight edge
Semicircle: 3.14 × 10 ÷ 2 + 10 = 25.7
Another way
(3.14 + 2) × diameter ÷ 2
(3.14 + 2) × 10 ÷ 2 = 25.7
In full
A perimeter is the length all the way round the outside: the curved parts from the circumference, the straight parts added one by one. Circumference = 3.14 × diameter. A semicircle's perimeter = half the circumference + the diameter: for a diameter of 10 cm, 3.14 × 10 ÷ 2 = 15.7, then 15.7 + 10 = 25.7 cm — don't forget the diameter. A quarter circle's perimeter = a quarter of the circumference + two radii. In a shape made of pieces, count only the outside edges, not the dashed lines inside. To get a diameter from a circumference, divide: 31.4 ÷ 3.14 = 10. Another way: a semicircle's perimeter = (3.14 + 2) × diameter ÷ 2, the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Take π as 3.14. A circle's circumference is 47.1 cm. How long is its diameter, in cm?
Show the answer and working
Answer: 15 cm
Circumference = 3.14 × diameter, so backwards: 47.1 ÷ 3.14 = 15.
Example 2
Find the perimeter of this quarter circle. (Take π as 3.14.) The answer is □ cm
Show the answer and working
Answer: 42.84
The curve is a quarter of the circumference: 3.14 × 24 ÷ 4 = 18.84; add two radii: 18.84 + 24 = 42.84.
Example 3
A semicircle with a diameter of 23 cm has a perimeter of 59.11 cm. (Take π as 3.14.)
True or false?
Show the answer and working
Answer: True
The perimeter is the curve and the diameter: 3.14 × 23 ÷ 2 + 23 = 59.11.
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