WAEC 2021 Mathematics · Question 3

A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. calculate…

Question

A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. calculate the area of the region not covered by the trapezium. π = $\frac{22}{7}$

A.84cm $^2$
B.80cm $^2$
C.30cm $^2$
D.94cm $^2$

Answer: C. 30cm $^2$

Explanation written with AI and checked against the answer key

Let me work through this carefully. Step 1: Area of the circle Area = πr² = (22/7) × 7 × 7 = 154 cm² Step 2: Area of the trapezium Area = ½(a + b)h = ½(10 + 21)(8) = ½ × 31 × 8 = 124 cm² Step 3: Area not covered 154 − 124 = 30 cm² A check on the geometry: A trapezium inscribed in a circle of radius 7 cm would have a diameter of 14 cm, so a parallel side of 21 cm cannot fit inside the circle, because a chord can never be longer than the diameter. The question as written is therefore geometrically inconsistent. Still, WASSCE expects you to use the given numbers, and the intended calculation is the one above. Answer: C. 30 cm² Tip: For "area not covered" questions, subtract the inscribed shape's area from the circle's area. Compute each area separately, then subtract. With π = 22/7 and r = 7, the 7s cancel, so the circle's area is always easy: 22 × 7 = 154.

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A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. calculate…

Question

Answer: C. 30cm2^22

Answer: C. 30cm $^2$