Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(
To calculate the surface area of a square pyramid, we need to find the area of the base and the lateral faces.
The base of the square pyramid is a square, so the area of the base is:
Base Area = length x width = 12 x 12 = 144
The lateral faces are four triangles, so the area of each lateral face is:
Lateral Face Area = 1/2 x base x height
In this case, the base of the lateral face is the side length of the base (12) and the height is the slant height (18).
Lateral Face Area = 1/2 x 12 x 18 = 108
Since there are four lateral faces, the total area of the lateral faces is:
Total Lateral Face Area = 4 x Lateral Face Area = 4 x 108 = 432
Finally, we can find the total surface area of the square pyramid by adding the area of the base and the total lateral face area:
Surface Area = Base Area + Total Lateral Face Area
Surface Area = 144 + 432
Surface Area = 576
Therefore, the surface area of the square pyramid is 576.