NumericalModerate2 marks
9(b)
The given figure represents a kite with a circular and a semicircular motifs stuck on it. The radius of a circle is 2.5 cm and the semicircle is 2 cm. If diagonals AC and BD are of lengths 12 cm and 8 cm respectively, find the area of the:
Shaded part. Give your answer correct to the nearest whole number.
Topic: Circle theorems
Previous-year question practice database
Answer
Exam answer
Area of kite = 1/2 × AC × BD = 1/2 × 12 × 8 = 48 cm².
Shaded area = area of circle + area of semicircle = π(2.5)² + 1/2 π(2)² = 6.25π + 2π = 8.25π ≈ 25.93 cm².
Nearest whole number:
Answer: Shaded area ≈ 26 cm².
Explanation
The shaded motifs consist of one full circle of radius 2.5 cm and one semicircle of radius 2 cm.
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