A1. A regular, right, quadrilateral prism has a surface area of $128 \mathrm{~m}^{2}$ and a height of $6 \mathrm{~m}$. What is the length of its space diagonal?
(A) $D \doteq 8.23 \mathrm{~m}$
(B) $D \doteq 8.24 \mathrm{~m}$
(C) $D \doteq 7.22 \mathrm{~m}$
(D) $D \doteq 8.25 \mathrm{~m}$
(E) $D \doteq 7.21 \mathrm{~m}$
A1. Using the formula for calculating the surface area of a regular quadrilateral prism $P=2 a^{2}+4 a v$, we obtain the quadratic equation $128=2 a^{2}+24 a$. The solutions to the quadratic equation are $a=4$ and $a=-16$. We determine that the correct solution is $a=4$. The base edge of the prism measures $a=4 \text{~m}$. Using the formula $D=\sqrt{2 a^{2}+v^{2}}$, we calculate the length of the space diagonal $D \doteq 8.25 \text{~m}$. The correct answer is $\mathrm{D}$.