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A regular pentagon has an area of 315.25 square meters, and each side of the pentagon measures 9.7 meters. What is the length of an apothem of the pentagon?

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Answer :

Answer:

Step-by-step explanation:

its 13

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The length of the apothem of the pentagon is 12.96 meters .

What is apothem ?
In geometry, the apothem of a polygon is the distance from the center of the polygon to the midpoint of one of its sides. For a regular polygon (a polygon with all sides and angles equal), the apothem is the perpendicular distance from the center of the polygon to one of its sides.

Explanation:
The formula for the area of a regular pentagon is:

A = (1/2)P × a

where A is the area, P is the perimeter, and a is the apothem.

To solve for the apothem, we need to rearrange the formula and solve for a:

a = (2A) / P

The perimeter of a regular pentagon is given by:

P = 5s

where s is the length of each side.

Substituting the given values, we get:

P = 5s = 5(9.7) = 48.5

A = 315.25

a = (2A) / P = (2 × 315.25) / 48.5 = 12.96

Therefore, the length of the apothem of the pentagon is 12.96 meters (rounded to two decimal places).

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