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
