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      Question

      In a semicircle, AB is the diameter and C is a point on

      the semicircle such that AC = 14 cm and BC = 28 cm. The region inside the semicircle but above triangle ABC is shaded. Find the area of the shaded region. (Use π = 22/7.)
      A 125 cm² Correct Answer Incorrect Answer
      B 189 cm² Correct Answer Incorrect Answer
      C 225 cm² Correct Answer Incorrect Answer
      D 135 cm² Correct Answer Incorrect Answer

      Solution

      Since AB is a diameter and C lies on the semicircle, ∠ACB = 90°. AC = 14, BC = 28 AB² = AC² + BC² = 14² + 28² = 196 + 784 = 980 r² = (AB²)/4 = 980/4 = 245 Area of semicircle = ½ × (22/7) × 245 = 385 cm² Area of △ABC = ½ × 14 × 28 = 196 cm² Shaded area = 385 − 196 = 189 cm²

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