Question

Question 9
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

Given : Octagon having eight equal sides, each 5 m
Construction : Divide the octagon into 3 figures, two trapezium whose parallel and perpendicular sides 11 m and 4 m respectively and third figure is rectangle having length and breadth 11 m and 5 m respectively

Area of the octagonal platform = Area of rectangle + Area of the two trapeziums

Now, Area of two trapeziums = $2\times \frac{1}{2}(a+b)\times h$
= $2\times \frac{1}{2}(11+5)\times 4=4\times 16=64m^2$
And Area of rectangle = length $\times$ breadth
= $11\times 5=55m^2$
$\therefore$ Total area of octagon = $64+55=119m^2$