To calculate the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.

Question

First, calculate the area of the base:
Area of a square = side length x side length
Area of the base = 12 x 12 = 144 square units

Next, calculate the area of each triangular face:
Area of a triangle = 0.5 x base x height
Since the base of each triangular face is the same as the side length of the square base (12) and the slant height is given as 18, we can calculate the height using the Pythagorean theorem:
height = sqrt(18^2 - 12^2) = sqrt(324 - 144) = sqrt(180) ≈ 13.42

Now, calculate the area of each triangular face:
Area of each triangular face = 0.5 x 12 x 13.42 ≈ 80.52 square units

Since there are four triangular faces, the total area of all the triangular faces is:
Total area of all triangular faces = 4 x 80.52 = 322.08 square units

Finally, calculate the total surface area of the square pyramid by adding the area of the base and the area of the four triangular faces:
Surface area = 144 + 322.08 = 466.08 square units

Therefore, the surface area of the square pyramid is 466.08 square units.
Can you reword and shorten this

Answer 1

To find the surface area of a square pyramid, calculate the area of the base (12 x 12 = 144 sq units) and the area of each triangular face (0.5 x 12 x 13.42 ≈ 80.52 sq units). Multiply the area of one triangular face by 4 to get the total area of all four faces (322.08 sq units). Add the base area and total triangular face area to get the total surface area of the pyramid (144 + 322.08 = 466.08 sq units).