Question

The top surface of a raised platform is in the shape of a regular octagaon as shown in the figure. Find the area of the octagonal surface.

• A. $119m^2$
• B. $97m^2$
• C. $183m^2$
• D. $153m^2$

Answer 1

The correct option is A $119m^2$

Area of the octagonal surface = area of trapezium ABCH + area of rectangle HCDG + area of trapezium GDEF

Area of trapezium ABCH = Area of trapezium GDEF
$=\frac{1}{2}(a+b)\times h$
$=\frac{1}{2}(11+5)\times 4$
$=\frac{1}{2}\left(16\right)\times 4$
$=32m^2$
$AreaofrectangleHCDG$
$=l\times b=11m\times 5m=55m^2$

$Areaoftheoctagonalsurface$
$=32m^2+55m^2+32m^2=119m^2$

$Hence,therequiredareais119m^2$