Question

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

Side of regular octagon $=5cm$

Area of trapezium $ABCH=$ Area of trapezium $DEFG$

Are of trapezium $ABCH=\frac{1}{2}\times$ (Sum of parallel sides) $\times$ Height

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

$=32m^2$

Area of rectangle $HGDC=11\times 5=55m^2$

Area of octagon $=$ Area of trapezium $ABCH+$ Area of trapezium $DEFG$

$+$ Area of rectangle $HGDC$

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

$=119m^2$