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WAEC Mathematics 2007 Question 50

Question 50

Mensuration of Plane Shapes

In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4 cm. Find the area of the shaded region.

Diagram for this question
  1. A.43.36 cm2
  2. B.32.07 cm2
  3. C.18.21 cm2
  4. D.6.93 cm2
Show the answer and explanation

Answer: C (18.21 cm2)

Explanation

Radius = 4 cm. Shaded = semicircle − triangle = ½ × 22/7 × 16 − ½ × 4 × 4 × sin 60° = 25.14 − 6.93 = 18.21 cm2.