Total surface area of a square pyramid: Slant height = 8 cm; base is a square of side 4 cm. Find the total surface area (cm^2).

Introduction / Context:For a right square pyramid, total surface area equals base area plus the sum of areas of four congruent triangular faces. Given slant height (not altitude), lateral area uses 1/2 * perimeter * slant height.

Given Data / Assumptions:

• Base side a = 4 cm → base area A_base = a^2 = 16 cm^2
• Slant height l = 8 cm
• Lateral area A_lat = (1/2) * (perimeter) * l = (1/2) * (4a) * l

Concept / Approach:Compute perimeter then lateral area; add to base area for TSA.

Step-by-Step Solution:Perimeter = 4 * 4 = 16 cmA_lat = (1/2) * 16 * 8 = 64 cm^2TSA = A_base + A_lat = 16 + 64 = 80 cm^2

Verification / Alternative check:Each triangular face area = (1/2) * base * slant height_along_face = (1/2) * 4 * 8 = 16; four faces → 64; adding base 16 → 80.

Why Other Options Are Wrong:64 ignores the base; 72, 84, 88 miscompute the lateral contribution or include extras not present.

Common Pitfalls:Confusing slant height with triangular altitude to the apex; forgetting the base area in TSA.

Final Answer:80