A high school is building a new gymnasium in the shape of a pyramid. Its base is a square with each side 500 feet long and has a slant height of 60 feet. What is the closest to the surface area of this pyramid?
280,000 ft2
265,000 ft2
490,000 ft2
310,000 ft2
The surface area of a pyramid is given by the formula A = (1/2)Pl + B, where P is the perimeter of the base, l is the slant height, and B is the area of the base.
For this pyramid, we know that P = 4(500) = 2000 and l = 60. The area of the base is simply 500^2 = 250,000.
Using these values in the formula, we get A = (1/2)(2000)(60) + 250,000 = 310,000.
Therefore, the closest answer is 310,000 ft2.