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Mathematics

Grade9

Easy

Question

The area of a regular pentagon is 440.44 square in, and the perimeter is 80 in. Find the length of the apothem of the pentagon.

11
22
33
44

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: 22

The area of a regular pentagon is 440.44 square in, and the perimeter is 80 in. Find the length of the apothem of the pentagon.
In the question it is given that,
Area of the regular pentagon= 440.44 square
Perimeter of the regular pentagon= 80 in
Here, we have to find the length of the apothem of the pentagon.
Area of the polygon = $fraction numerator 1 over denominator 2 end fraction$ ×Apothem× Perimeter of the polygon
$rightwards double arrow$ 440.44 = $fraction numerator 1 over denominator 2 end fraction$ × a×80
$rightwards double arrow$ a= $fraction numerator 440.44 cross times 2 over denominator 80 end fraction$
$rightwards double arrow$ a = 11
So, the length of the apothem of the pentagon is 11.
Therefore, the correct option is a, i.e., 11.

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