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.

We can observe, Area of the octagonal surface= area of trapezium ABCH + area of rectangle HCDG + area of trapezium GDEF
Finding area of different parts:

Area of trapezium ABCH = Area of trapezium GDEF

\(=\frac { 1 }{ 2 }\times (a + b) \times h\)

\(=\frac { 1 }{ 2 }\times (11 + 5) \times 4\)

\(=\frac { 1 }{ 2 }\times 16 \times 4\)

\(= 32 m^2\)

Area of rectangle HCDG =\( l \times b = 11 m \times 5 m = 55 m^2\)

Area of the octagonal surface = \(32 m^2 + 55 m^2 + 32 m^2 = 119 m^2\)

Hence, the required area = \(119 m^2\).