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: 40000C: 69545 D: 98774

Answer:DStep-by-step 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 = [tex]\frac{3\sqrt{3}a^{2} }{2}[/tex]Where a is the side length (which is 50)Hence,Area of Hexagon = [tex]\frac{3\sqrt{3}a^{2} }{2}=\frac{3\sqrt{3}(50)^{2} }{2}=6495.2[/tex]Also, area of Nonagon is given by  [tex]6.1818*s^2[/tex]Where s is the length of the sideHence,Area of Nonagon = [tex]6.1818*s^2=6.1818*(50)^2=15,454.5[/tex]Total floor area = 6495.2 + 15,454.5 = 21,949.7Hence,Total Cost = 21,949.7 * 4.5 = 98,773.65THis is closest to the answer choice D.