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) in a essay

Answer 1

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.

First, we need to find the area of the base, which is a square. Since the base length is 12, the area of the base can be calculated by squaring the base length:
Area of base = 12^2 = 144

Next, we need to find the area of each triangular face. The slant height is given as 18, and the base length is 12. Since the base and the slant height form a right-angled triangle, we can use the Pythagorean theorem to find the height of each triangular face:
height = sqrt(18^2 - 6^2)
height = sqrt(324 - 36)
height = sqrt(288)
height = 16.97

Now, we can calculate the area of one triangular face using the base length and height:
Area of one triangular face = (1/2) * base length * height
Area of one triangular face = (1/2) * 12 * 16.97
Area of one triangular face = 101.82

Since there are four triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 4 * Area of one triangular face
Total area of triangular faces = 4 * 101.82
Total area of triangular faces = 407.28

Finally, we can calculate the total surface area of the square pyramid by adding the area of the base and the area of the triangular faces:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 144 + 407.28
Total surface area = 551.28

Therefore, the surface area of the square pyramid with a base length of 12 and a slant height of 18 is 551.28.