Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(2 points) write it in your own words please.
To calculate the surface area of a square pyramid, we need to find the sum of the areas of the base and the four triangular faces.
1. First, calculate the area of the base by using the formula for the area of a square: base length squared.
Area of base = 12^2 = 144 square units
2. Next, calculate the area of one of the triangular faces by using the formula for the area of a triangle: 1/2 base times height.
Since the base of the triangle is the same as the base of the square (12), we can calculate the height using the Pythagorean theorem:
height = sqrt(18^2 - 6^2) = sqrt(324 - 36) = sqrt(288) = 12√2
Now, calculate the area of one triangular face:
Area of one triangular face = 1/2 * 12 * 12√2 = 72√2 square units
3. Finally, calculate the total surface area by summing the area of the base and the areas of the four triangular faces:
Surface area = Area of base + 4(Area of one triangular face)
Surface area = 144 + 4(72√2) = 144 + 288√2 ≈ 595.33 square units
Therefore, the surface area of the square pyramid is approximately 595.33 square units.