Final answer:
To calculate the total surface area of the square pyramid, add the area of the base square (64 cm²) to the area of the four triangular faces (96 cm²), resulting in a total surface area of 160 cm².
Step-by-step explanation:
The student has asked to find the total surface area of a square pyramid with a base side length of 8 cm and a slant height of 6 cm. To calculate the surface area (SA) of a square pyramid, we need to find the area of the base and the area of all four triangular faces.
Firstly, the area of the base (which is a square) is found by squaring the length of one side:
Base area = side · side = 8 cm · 8 cm = 64 cm².
Then, to find the area of one triangular face, we use the formula for the area of a triangle:
Area of a triangle = 1/2 · base · height. Here, the base of each triangle is the side of the square, and the height is the slant height of the pyramid:
Area of one triangular face = 1/2 · 8 cm · 6 cm = 24 cm².
Since the pyramid has four triangular faces, we multiply the area of one triangular face by four:
Total area of triangular faces = 4 · 24 cm² = 96 cm².
Finally, we add the area of the base to the total area of the triangular faces to find the total surface area:
Total surface area (SA) = Base area + Total area of triangular faces = 64 cm² + 96 cm² = 160 cm².