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Primary 6 · Circle · Question type 6.4

P6 Circle: Perimeter of a Rectangle with a Semicircle

When two shapes are joined, exclude their shared edge from the perimeter because it is inside the figure.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Circle chapter9 question types · see the chapter

The lesson · 2 minutes 5 seconds

How do you find the perimeter of a rectangle and semicircle in P6?

Watch: the perimeter of a rectangle with half a circle joined to one end

Another worked example

A worked example

A notice board is a rectangle 40 cm long and 24 cm wide. Its two top corners are rounded off by quarter circles of radius 4 cm, and its two bottom corners by quarter circles of radius 8 cm. Find the perimeter of the board. (Take π = 3.14.)

The working · Nine lines

The step-by-step working

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

  1. circumference = π × d
  2. top corner diameter = 4 × 2 = 8
  3. bottom corner diameter = 8 × 2 = 16
  4. two top arcs = 2 × 1/4 × 3.14 × 8 = 12.56
  5. two bottom arcs = 2 × 1/4 × 3.14 × 16 = 25.12
  6. top edge left = 40 - 4 - 4 = 32
  7. bottom edge left = 40 - 8 - 8 = 24
  8. two side edges left = 2 × (24 - 4 - 8) = 24
  9. perimeter = 12.56 + 25.12 + 32 + 24 + 24 = 117.68

The answer is 117.68 cm.

Practise · Modelled on top school exam questions

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A border made from circular arcs

Combine the two semicircular arcs with the two straight ends.

The figure shows a half ring made from two semicircles with the same centre, standing on the same straight line. The outer semicircle has a radius of 10 cm and the inner one a radius of 6 cm. The band between them is shaded. Find the perimeter of the shaded band. (Take π = 3.14.)

cm

Show the step-by-step solution
  1. circumference = π × d
  2. outer diameter = 10 × 2 = 20
  3. inner diameter = 6 × 2 = 12
  4. outer arc = 1/2 × 3.14 × 20 = 31.4
  5. inner arc = 1/2 × 3.14 × 12 = 18.84
  6. one end = 10 - 6 = 4
  7. perimeter = 31.4 + 18.84 + 4 + 4 = 58.24

Ans: 58.24 cm

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Next, subtract a cut-out region from a whole figure. Area Left When a Circle Is Cut from a Square →

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