The 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.

We have a regular octagon. In a regular octagon, all 8 sides are equal in length.
Given: Length of each side = 5 m

Now if we break the figure, we get two trapezium and one rectangle.

In both the trapezium,
First parallel line = 11 m
Second parallel line = 5 m
Height = 4 m
Here, both trapeziums have the same area.

So, the area of two Trapezium

$=2\left[\frac{1}{2}\left(\mathrm{Sum} \mathrm{of} \mathrm{parallel} \mathrm{sides}\right)\times \mathrm{Height}\right]$

$=2\left[\frac{1}{2}\left(11+5\right)\times 4\right]$

$=64 {\mathrm{m}}^2$

Now, in rectangle CDEF,

Length = 11 m, 
Breadth = 5 m

So, area of rectangle = length × breadth
$=11\times 5$
$=55\mathrm{ }{\mathrm{m}}^2$

Now the overall area of the octagon

= Area of two Trapezium + Area of rectangle
= 64 + 55
= 119 m²