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.
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.
make it shorter
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.