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.

Given: Octagon having eight equal sides, each 5 m

Construction: Divided the octagon in 3 figures, two trapeziums whose parallel and perpendicular sides are 11 m and 4 m respectively and third figure is rectangle having length and breadth 11 m and 5 m respectively.

Now Area of two trapeziums = 2 x 1/2 × (a + b) h

= (11 + 5) × 4

= 64 sq. m

And Area of rectangle = length × breadth

= 11 × 5

= 55 sq. m

∴ Total area of octagon = 64 + 55

= 119 sq. m