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. Make it look like a seventh grader did it.

Answer 1

make it shorter

Answer 2

First, we need to calculate the area of the base of the pyramid, which is a square.

The formula for the area of a square is side x side. Since the base length is 12, we will plug that in:

Base Area = 12 x 12
Base Area = 144

Now we need to calculate the area of each of the four triangles on the slant sides of the pyramid. The formula for the area of a triangle is 1/2 x base x height. Since the base of each triangle is 12 and the slant height is 18, we can plug that in:

Triangle Area = 1/2 x 12 x 18
Triangle Area = 6 x 18
Triangle Area = 108

Because there are four triangles, we need to multiply the area of one triangle by 4 to get the total area of all four triangles:

4 x 108 = 432

Now we can calculate the total surface area by adding the area of the base and the total area of the triangles:

Total Surface Area = Base Area + Triangle Area
Total Surface Area = 144 + 432
Total Surface Area = 576

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

Answer 3

Area of base = 12 x 12 = 144

Area of each triangle = 1/2 x 12 x 18 = 108
Total area of all four triangles = 4 x 108 = 432

Total surface area = 144 (base) + 432 (triangles) = 576

The surface area of the square pyramid is 576 square units.