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Mathematics

Grade9

Easy

Question

Find the area of the regular octagon.

565
600
696
740

hint Hint:

Polygon is a two- dimensional closed figure which is made up of three or more line segments. Each polygon has its own properties based on the number of sides. Area of a regular polygon can be determined using the formula $A r e a space o f space t h e space p o l y g o n equals 1 half cross times P e r i m e t e r space o f space t h e space p o l y g o n cross times A p o t h e m$ . Here, we have to find the area of the given polygon.

The correct answer is: 696

In the question there is a polygon as shown in the figure.
Here, we have to find the area of the given polygon.
From the given figure we can say that,
Length of each side of the octagon= 12
Apothem= 14.49
Perimeter of the octagon= Length of each side of the octagon $cross times$ No. of sides
= 12 $cross times$ 8
= 96
Now,
Area of the polygon= $1 half cross times P e r i m e t e r space o f space t h e space p o l y g o n cross times A p o t h e m$
= $1 half cross times 96 cross times 14.49$
= 695.52
So, the area of the given polygon is aproximately equal to 696.
Therefore, the correct option is c, i.e., 696.

A perpendicular line segment joining the centre and one of the sides of the regular polygon is called apothem of the polygon.

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