The surface area of a pyramid is the sum of which components?

The surface area of a pyramid is the sum of which components?

• A. Base Area × Lateral Area
• B. Base Area minus Lateral Area
• C. Base Area + Lateral Area
• D. Base Area × h

Answer: (C)

Think of a pyramid as a base polygon with triangular faces wrapped around it. The base area is the flat footprint, and the lateral area is the total area of all those triangular side faces. The total surface area is all exterior surface, so you add the base area to the lateral area. That is why the surface area is base area plus lateral area. The other forms don’t fit because they involve multiplying areas or mixing in height, which doesn’t correspond to summing the actual exposed surfaces. For a quick check, if the base is a square of side s and the slant height of each triangular face is l, the surface area would be s^2 + 4*(1/2*s*l) = s^2 + 2 s l.

Think of a pyramid as a base polygon with triangular faces wrapped around it. The base area is the flat footprint, and the lateral area is the total area of all those triangular side faces. The total surface area is all exterior surface, so you add the base area to the lateral area. That is why the surface area is base area plus lateral area. The other forms don’t fit because they involve multiplying areas or mixing in height, which doesn’t correspond to summing the actual exposed surfaces. For a quick check, if the base is a square of side s and the slant height of each triangular face is l, the surface area would be s^2 + 4*(1/2sl) = s^2 + 2 s l.