Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
Solution and Explanation
Side of regular octagon = 5 cm
Area of trapezium ABCH = Area of trapezium DEFG
Area of trapezium ABCH = \(\frac{1}{2} × \)(AB + CH) \(×\) AI
\(= \frac{1}{2} ×\) (5 m + 11 m) \(×\) 4 m
\(= \frac{1}{2} ×\) 16 m \(×\) 4 m
= 32 m²
Area of rectangle HGDC \(= 11 × 5 = 55\) m2
Area of octagon = Area of trapezium ABCH + Area of trapezium DEFG + Area of rectangle HGDC
= 32 m2 + 32 m2 + 55 m2 = 119 m2
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