WAEC Mathematics 2023 Theory — Question 3
Question 3 of 13 from the West African Examinations Council (WAEC) Mathematics 2023 Theory paper, with the correct answer and a full explanation.
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3. Since PQR is an equilateral triangle, all sides and angles are the same, thus each angle θ=60°. Area of triangle PQR = (1/2)|PQ||QR|sinθ.
Model answer
Area of triangle PQR=(1/2)×18×18×sin60°=(1/2)×18×18×(√3/2)=140.2961 cm². Area of sector PAMB=(θ/360)×πr²=(60/360)×(22/7)×|mp|²=127.2857 cm² (using r=mp, the radius of the arc). Area of shaded region=Area of triangle PQR - Area of sector PAMB=140.2961-127.2857=13.01 cm² (2 d.p.).
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