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