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Mathematics

Grade9

Easy

Question

The area of a regular octagon is 695.3 square cm, and the sides are 12 cm. What is the length of the apothem?

17.2
14.5
13.9
12.6

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 apothem of the given polygon using the area formula.

The correct answer is: 14.5

In the question it is given that,
Area of a regular octagon= 695.3 square cm
Length of each side= 12 cm
Here, we have to find the length of the apothem.
Perimeter of the polygon = Length of each side × No. of sides
=12×8
= 96
Now,
Area of the polygon = $1 half cross times P e r i m e t e r space o f space t h e space p o l y g o n cross times A p o t h e m$
695.3 = $fraction numerator 1 over denominator 2 end fraction$ ×96× Apothem
= $fraction numerator 695.3 cross times 2 over denominator 96 end fraction$
=14.5
So, the length of the apothem of the polygon is 14.5.
Therefore, the correct option is b, i.e., 14.5.

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