A regular square pyramid has base perimeter p=20, slant height l=5, and base area b=25. What is its surface area?

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Multiple Choice

A regular square pyramid has base perimeter p=20, slant height l=5, and base area b=25. What is its surface area?

Explanation:
For a regular square pyramid, the surface area is the base area plus the lateral area (the area of the four triangular faces). The base perimeter is 20, so the side length of the square base is 20/4 = 5, and the base area is 5^2 = 25. Each triangular face uses the base edge as its base (length 5) and the slant height as its height (5), so one triangle has area (1/2) × 5 × 5 = 12.5. With four faces, the lateral area is 4 × 12.5 = 50. Add the base area: 25 + 50 = 75. The surface area is 75.

For a regular square pyramid, the surface area is the base area plus the lateral area (the area of the four triangular faces). The base perimeter is 20, so the side length of the square base is 20/4 = 5, and the base area is 5^2 = 25.

Each triangular face uses the base edge as its base (length 5) and the slant height as its height (5), so one triangle has area (1/2) × 5 × 5 = 12.5. With four faces, the lateral area is 4 × 12.5 = 50.

Add the base area: 25 + 50 = 75. The surface area is 75.

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