Question

question 15 (multiple choice worth 4 points) (06.04r mc) what is the surface area of a square prism with sides that measure 8 units? 254 units² 300 units² 314 units² 384 units²

Explanation:

Step1: Recall surface - area formula

A square prism has 2 square bases and 4 rectangular lateral faces. If the side of the square base and the height of the prism are \(a = 8\) units, the area of one square base \(A_{base}=a^{2}\), and the area of one rectangular face \(A_{face}=a\times a\). The surface - area formula \(S = 2A_{base}+4A_{face}\).

Step2: Calculate area of base

\(A_{base}=a^{2}=8^{2}=64\) square units.

Step3: Calculate area of lateral face

\(A_{face}=a\times a = 8\times8 = 64\) square units.

Step4: Calculate surface area

\(S=2\times64 + 4\times64=(2 + 4)\times64=6\times64 = 384\) square units.

Answer:

D. 384 units²