In the surface area formula Ph + 2B, P stands for what?

• A. Base area
• B. Perimeter of the base
• C. Power of base
• D. Product of base sides

Answer: (B)

The idea is that a prism’s surface area comes from two parts: the sides around the outside and the two congruent bases. The term Ph accounts for all the side faces. Here, you multiply the distance around the base (the perimeter) by the height of the prism to get the total area of the side faces.

So P is the perimeter of the base—the whole length around the base. For a rectangular base with sides a and b, that perimeter is 2(a + b).

For example, if the base is 3 by 4 and the height is 5, the base perimeter is 2(3 + 4) = 14, so Ph = 14 × 5 = 70. The base area is B = 3 × 4 = 12, so 2B = 24. The total surface area is 70 + 24 = 94.

The base area plays separately as 2B because there are two bases, while the perimeter times height covers the side surfaces. This distinguishes perimeter from base area and from any unrelated notion like a power.