Question

Be awesome! Is a new cross fit gym in town. The gym is almost set to its grand opening. The contractors are doing flooring. Gymnasium flooring cost $4.50 per square foot. The gym has 2 main rooms, one in a shape of a regular hexagon and the other in a shape of a regular nonagon. Both rooms have side lengths of 50 feet. Which of the following represents the closest estimate for the total of gymnasium flooring material? A: 29229 B: 40000

C: 69545 D: 98774

Answer 1

D

Explanation:

We need to find total area of the two rooms (hexagon and nonagon) and then multiply that by 4.5 to get total cost.

Area of Hexagon =
`(3√(3)a^(2) )/(2)`

Where a is the side length (which is 50)

Hence,

Area of Hexagon =
`(3√(3)a^(2) )/(2)=(3√(3)(50)^(2) )/(2)=6495.2`

Also, area of Nonagon is given by
`6.1818*s^2`

Where s is the length of the side

Hence,

Area of Nonagon =
`6.1818*s^2=6.1818*(50)^2=15,454.5`

Total floor area = 6495.2 + 15,454.5 = 21,949.7

Hence,

Total Cost = 21,949.7 * 4.5 = 98,773.65

THis is closest to the answer choice D.