Theory question 110
Mensuration of Plane Shapes(a) Solve: (x − 2)(x − 3) = 12.
(b) In the diagram, M and N are the centres of two circles of equal radii 7 cm. The circles intercept at P and Q. If ∠PMQ = ∠PNQ = 60°, calculate, correct to the nearest whole number, the area of the shaded portion. [Take π = 22/7].
Show the model answer
Model answer
(a) x2 − 5x + 6 = 12 → x2 − 5x − 6 = 0 → (x − 6)(x + 1) = 0 → x = 6 or x = −1.
(b) One segment = sector − triangle = 60/360 × 22/7 × 72 − ½ × 72 × sin 60° = 25.667 − 21.218 = 4.449 cm2.
The shaded part is two such segments: 2 × 4.449 ≈ 8.9 ≈ 9 cm2.
Explanation
The shaded lens is made of two equal segments, one from each circle.