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# 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 = $$119 m^2$$.