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Q.

Top surface of a raised platform is in the shape of a regular octagon as shown in figure. Find the area of the octagonal surface.

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a

b

c

d

answer is B.

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Detailed Solution

Concept- A regular octagon is indeed a closed figure with the same length sides and internal angles. It does have eight lines of reflective symmetry and order 8 rotational symmetry.
The view is from top of the surface. We know the sum of exterior angles will be

.
For finding the angle subtended by each side we will simply divide the total angle into 8 parts.
Angle subtended at the center

We first find area of one triangle and by which we can simply find the area of whole octagon, for this take a section of a triangle shown below and just dram a perpendicular bisector OX on line FE

Question Image

We know the perpendicular bisector split the angle and side into two equal parts.

When applying the trigonometric function,

When putting the value of

in (1), we get

When cross multiplying, we will get

Now, area of triangle

Therefore, Area of regular octagon

Hence, the correct answer is option 2)

.

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