Final answer:
The correct answer is option d. To find the surface area of a square pyramid with a side length of 5 inches and a slant height of 6 inches, calculate the area of the square base and the total area of the four triangular faces. The base area is 25 in² and the area of the four triangles is 60 in². The correct total surface area is 85 in².
Step-by-step explanation:
The objective is to calculate the surface area of a square pyramid with a side length of 5 inches and a slant height of 6 inches. A square pyramid has one square base and four triangular faces. To find the total surface area, we combine the area of the base with the areas of the triangular faces.
To find the area of the base, which is a square, we use the formula:
Area of the square base = side length × side length
= 5 in × 5 in
= 25 in².
To find the area of one of the triangular faces, we use the formula for the area of a triangle:
Area of a triangular face = 0.5 × base × slant height
= 0.5 × 5 in × 6 in
= 15 in².
Since there are four identical triangular faces, we multiply the area of one triangle by four:
Total area of the four triangles = 15 in² × 4
= 60 in².
Finally, we add the area of the base to the total area of the triangles to find the total surface area:
Total surface area = area of the square base + total area of the four triangles
= 25 in² + 60 in²
= 85 in².
Therefore, the correct option is d. 85 in².