Theory question 103
Mensuration of Plane ShapesIn the diagram, PQR is an equilateral triangle of side 18cm. M is the midpoint of QR. An arc of a circle with centre P touches QR at M and meets PQ at A and PR at B. Calculate, correct to two decimal places, the area of the shaded region. [Take π = 22/7]
Show the model answer
Model answer
Radius PM = height of triangle = 18 sin 60° = 9√3 ≈ 15.588 cm
Area of triangle PQR = ½ × 18 × 18 × sin 60° = 81√3 ≈ 140.30 cm²
Area of sector PAB (angle 60°) = 60/360 × 22/7 × 243 ≈ 127.29 cm²
Shaded area = 140.30 − 127.29 ≈ 13.01 cm²
Explanation
The radius of the arc is the height PM of the triangle.