Surface Area Unit Test
calculate the surface of the square pyramid that has a base length of 12 and a slant height of 18
To calculate the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
1. Area of the base:
Since the base of the pyramid is a square with a side length of 12, the area of the base is 12^2 = 144 square units.
2. Area of each triangular face:
The slant height of the pyramid is 18, and the height of each triangular face can be found using the Pythagorean theorem:
h = sqrt(18^2 - 6^2) = sqrt(324 - 36) = sqrt(288) = 12√2
The area of each triangular face is (1/2)(base)(height) = (1/2)(12)(12√2) = 72√2 square units.
3. Total surface area:
There are four triangular faces in a pyramid, so the total surface area is:
4(72√2) + 144 = 288√2 + 144 ≈ 584.97 square units.
Therefore, the surface area of the square pyramid is approximately 584.97 square units.