Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(2 points)
Math Short Answer Rubric (2 points)
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 area of the base (a square) can be calculated by squaring the base length:
Base area = (12)^2 = 144
The area of one of the triangular faces can be calculated using the formula for the area of a triangle:
Face area = 1/2 * base length * slant height = 1/2 * 12 * 18 = 108
Since there are four triangular faces on a square pyramid, the total area of all four faces is:
Total face area = 4 * 108 = 432
Therefore, the total surface area of the square pyramid is the sum of the base area and the total face area:
Surface area = Base area + Total face area
Surface area = 144 + 432
Surface area = 576
So, the surface area of the square pyramid is 576.