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Beth needs to fertilize her flowerbed, which is in the shape of a regular pentagon. A bag of fertilizer states that it can fertilize up to 150 square feet, but Beth is not sure how many bags of fertilizer she should buy. Each side of the pentagon is 15 feet long

Respuesta :

Answer: he should buy 3 bags

Step-by-step explanation:

In order to determine the area of the flower bed which has the shape of a Pentagon, we would apply the formula for determining the area of a polygon which is expressed as

Area = (perimeter × apotherm)/2

The apotherm is the perpendicular distance from the center of the polygon. The formula for determining the apotherm is

Apotherm = S/2tan(180/n)

Where

S = side length of the polygon

n = number of sides of the polygon.

From the information given,

S = 15 feet

n = 5

Apotherm = 15/2tan(180/5) = 10.3 ft

Perimeter = side length × number of sides

Perimeter = 15 × 5 = 75 ft

Therefore,

Area of the Pentagon = 75 × 10.3/2 = 386.25 ft²

A bag of fertilizer states that it can fertilize up to 150 square feet. Therefore, the number of bags that he can buy is

386.25/150 = 2.575 bags

He should buy approximately 3 bags

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