in the figure the centre of the circle is A and ABCDEF is a rectangular side hexagon of side 6 cm find area of segment BPF and area of shaded portion
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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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