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?
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
To find the surface area of a pyramid, you need to find the area of each triangular face and add them all up. Since this pyramid has a square base, there are four identical triangular faces.
To find the area of each triangular face, you can use the formula 1/2 base x height, where the base is one of the sides of the square base (500 ft) and the height is the slant height (60 ft).
Area of each triangular face = 1/2 x 500 ft x 60 ft = 15,000 ft2
Surface area of pyramid = 4 x Area of each triangular face = 4 x 15,000 ft2 = 60,000 ft2
Therefore, the closest answer choice is 65,000 ft2.