Question

In the figure, the centre of the circle is A and ABCDEF
is a rectangular hexagon of side 6 cm. Find :
(i) Area of segment BPF.
(ii)Area of the shaded portion.​

Answer 1

Area of segment BPF = 22.11 cm , Area of the shaded portion = 77.85 cm²

Step-by-step explanation:

Hexagon internal  angle = 120°

Hexagon side =Radius = 6 cm

Area of arc segment ABPF = (120/360)π R²

= (1/3) (3.14)6²

= 37.68 cm²

Area of ΔABF  = (1/2) 6 * 6*Sin(120/2)  =   18√3/2 = 9 * 1.73 = 15.57 cm²

Area of segment BPF = 37.68 - 15.57

= 22.11 cm

Area o hexagon  = (3√3 / 2)6² = 93.42 cm²

Area of the shaded portion. = 93.42 - 15.57 = 77.85 cm²

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