To calculate the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces.
1. The area of the base:
The base of the square pyramid is a square, so to find the area, you need to square the base length:
Base Area = 12^2 = 144 sq units
2. The area of each triangular face:
Each triangular face is a right triangle with a base of 12 and a height equal to the slant height.
Using the Pythagorean theorem, we can find the height of each triangular face:
Height = sqrt(18^2 - 12^2)
Height = sqrt(324 - 144)
Height = sqrt(180)
Height = 6*sqrt(5)
Now, we can find the area of one triangular face:
Face Area = (1/2) * base * height
Face Area = (1/2) * 12 * 6*sqrt(5)
Face Area = 36*sqrt(5) sq units
3. The total surface area:
Total Surface Area = Base Area + 4 * Face Area
Total Surface Area = 144 + 4 * 36*sqrt(5)
Total Surface Area = 144 + 144*sqrt(5)
Total Surface Area ≈ 433.88 sq units
So, the surface area of the square pyramid is approximately 433.88 square units.
A) Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.
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