A square-based pyramid has base side lengths of 45 feet and a slant height of 20 feet. What is the surface area of its sides, not including the base?
1800 ft²
450 ft²
900 ft²
3600 ft²
To find the surface area of the sides of the square-based pyramid, we need to find the area of each triangular side and multiply it by 4 since there are 4 triangular sides.
The formula to find the area of a triangle is A = (1/2)bh, where A is the area, b is the base, and h is the height.
In this case, the base is one side length of the square, so b = 45 feet.
The height can be found using the Pythagorean theorem since we know the slant height (20 feet) and one of the sides of the triangle (45 feet).
Using the Pythagorean theorem:
h² + (45/2)² = 20²
h² + 2025/4 = 400
h² = 400 - 2025/4
h² = 1600/4 - 2025/4
h² = -425/4
Since a negative length does not make sense, we can conclude that there is no triangle with the given side lengths. Therefore, it is not possible to construct a square-based pyramid with a side length of 45 feet and a slant height of 20 feet.
The correct answer is that a pyramid with these dimensions is not possible, so the surface area of its sides, not including the base, is 0 ft².