Theory question 108
Mensuration of Plane ShapesIn the diagram, ABCDEO is two-thirds of a circle centre O. The radius AO is 7 cm and |AB| = |BC| = |CD| = |DE|. Calculate, correct to the nearest whole number, the area of the shaded portion. (Take π = 22/7)
Show the model answer
Model answer
Two-thirds of a circle is 240°, shared by 4 equal chords: each chord subtends 60° at O.
Area of one sector = 60/360 × 22/7 × 72 = 25.67 cm2.
Area of one triangle = ½ × 7 × 7 × sin 60° = 21.22 cm2.
Shaded area = 4 × (25.67 − 21.22) = 4 × 4.45 ≈ 17.8 cm2 ≈ 18 cm2.
Explanation
Each shaded segment = sector − triangle.