Final answer:
To find the surface area of a square base pyramid, we calculate the area of one face and multiply it by the number of faces. In this case, the surface area is 650.88 ft².
Step-by-step explanation:
To find the surface area of a square base pyramid, we need to calculate the area of each face and add them up. In this case, the pyramid has a square base with side lengths of 16.8 ft.
The slant height of the pyramid is given as 19.3 ft. S
ince it is a square base pyramid, all the faces are identical. So, to find the surface area, we can find the area of one face and multiply it by the number of faces.
The area of a triangle, with base b and height h, is given by the formula A = 1/2 * b * h. In this case, one face of the pyramid is a triangle with base equal to the side length of the base (16.8 ft) and height equal to the slant height (19.3 ft). So, the area of one face is
A = 1/2 * 16.8 ft * 19.3 ft = 162.72 ft².
Since there are four triangular faces in a square base pyramid, the total surface area is given by: surface area = 4 * area of one face = 4 * 162.72 ft² = 650.88 ft².
Therefore, the correct answer is A) 971.8 ft².