Question

A pyramid-shaped building is 318 ft tall and has a square base with sides of 580 ft. The sides of the building are made

from reflective glass. What is the surface area of the reflective glass?
The surface area of the glass is _____ ft².
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places
as needed.)

Answer 1

499,237 ft²

Explanation:

You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.

Area

To find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:

A = 1/2bh

There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:

4A = 4(1/2bh) = 2bh

Slant height

The slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)

h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet

Glass area

lateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²

The surface area of the glass is about 499237 square feet.