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Primary 6 · Circle · Question type 6.3

P6 Circle: Perimeter of Semicircles and Quarter Circles

The perimeter of a semicircle or quarter circle includes both the arc and the new straight edges.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Circle chapter9 question types · see the chapter

The lesson · 3 minutes 1 second

How do you find the perimeter of semicircles and quarter circles in P6?

Watch: the perimeter of a semicircle, then of a quarter circle

Another worked example

A worked example

A pizza has a 3/4 piece left, cut from its centre. The piece has a radius of 10 cm. Find the perimeter of the piece. (Take π = 3.14.)

The working · Four lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. circumference = π × d
  2. diameter = 10 × 2 = 20
  3. arc = 3/4 × 3.14 × 20 = 47.1
  4. perimeter = 47.1 + 10 + 10 = 67.1

The answer is 67.1 cm.

Practise · Modelled on top school exam questions

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The edges of a quadrant

Include the curved edge and both straight radii, leaving the answer in terms of pi.

A quarter circle has a radius of 8 cm. Find the perimeter of the quarter circle, leaving your answer in terms of π.

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Show the step-by-step solution
  1. circumference = π × d
  2. diameter = 8 × 2 = 16
  3. arc = 1/4 × π × 16 = 4π
  4. two radii = 8 + 8 = 16
  5. perimeter = 4π + 16

Ans: (4π + 16) cm

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Next, exclude the joined edge inside a composite figure. Perimeter of a Rectangle with a Semicircle →

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