Question

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.

 

Answer 1

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