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Mathematics

Grade9

Easy

Question

Find the area of the regular polygon.

$36 \sqrt{3}$
$42 \sqrt{3}$
56
$24 \sqrt{3}$

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 $A r e a equals 1 half cross times P e r i m e t e r space o f space t h e space p o l y g o n cross times A p o t h e m$ . Here, we have to find the area of the given polygon.

The correct answer is: $36 square root of 3$

In the question there is a polygon as shown in the figure above.
Here, we have to find the area of the given polygon.
From the figure we can say that,
Apothem= $2 square root of 3$
Length of each side=12
Perimeter of the given polygon= Length of each side $cross times$ No. of sides
Perimeter= 12 $cross times$ 3
So, Area of the polygon= $1 half cross times P e r i m e t e r space o f space t h e space p o l y g o n cross times A p o t h e m$
A = $fraction numerator 1 over denominator 2 end fraction$ × $2 square root of 3$ × (12×3) = $36 square root of 3$
So, the area of the given polygon is $36 square root of 3$ .
Therefore, the correct option is a, i.e., $36 square root of 3$ .

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