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Primary 6 · Circle · Question type 6.9

P6 Circle: Difference between Overlapping Regions

If two regions contain the same overlap, their difference equals the difference between the two whole shapes.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Circle chapter9 question types · see the chapter

The lesson · 4 minutes 20 seconds

How do you find the difference between overlapping regions in P6?

Watch: the difference between two regions where a square and a circle overlap

Another worked example

A worked example

The figure shows a semicircle of diameter 40 cm overlapping a square. Region X is the part of the semicircle that lies outside the square, and region Y is the part of the square that lies outside the semicircle. The area of X is 228 cm² more than the area of Y. Find the length of one side of the square. (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. area = π × r × r
  2. X = semicircle - S
  3. Y = square - S
  4. X - Y = semicircle - square
  5. radius = 40 ÷ 2 = 20
  6. semicircle = 1/2 × 3.14 × 20 × 20 = 628
  7. square = 628 - 228 = 400
  8. side × side = 400
  9. side = 20

The answer is 20 cm.

Practise · Modelled on top school exam questions

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Cancel the common overlap

The shared part belongs to both regions, so it cancels when their difference is found.

The figure shows a circle of radius 15 cm and a square of side 24 cm drawn so that they overlap. Region X is the part of the circle that lies outside the square, and region Y is the part of the square that lies outside the circle. Find the difference between the area of X and the area of Y. (Take π = 3.14.)

cm²

Show the step-by-step solution
  1. area = π × r × r
  2. X = circle - S
  3. Y = square - S
  4. X - Y = circle - square
  5. circle = 3.14 × 15 × 15 = 706.5
  6. square = 24 × 24 = 576
  7. X - Y = 706.5 - 576 = 130.5

Ans: 130.5 cm²

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