Question

Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.

Draw out the problem. Show your work solving each step. Find the area of the base and the area of the triangles x 4. Add the together. You may submit corrections via webmail for additional points. Please complete correction and send in a webmail to Mrs. Hadden.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

The base of the pyramid is a square, so the area of the base is:
Area of base = side length squared
Area of base = 12^2
Area of base = 144 square units

Next, we need to find the area of the four triangular faces. Each face is a triangle with base length equal to the side length of the base (12) and height equal to the slant height of the pyramid (18). The area of each triangle is:
Area of triangle = 1/2 * base * height
Area of triangle = 1/2 * 12 * 18
Area of triangle = 108 square units

There are four triangular faces, so the total area of all the triangular faces is:
Total area of triangular faces = 4 * 108
Total area of triangular faces = 432 square units

Finally, we can calculate the total surface area of the pyramid by adding the area of the base and the area of the triangular faces:
Surface area = Area of base + Total area of triangular faces
Surface area = 144 + 432
Surface area = 576 square units

Therefore, the surface area of the square pyramid is 576 square units.