Question

Select the correct answer.Christi is using a display box shaped like a regular pentagonal prism as a gift box. About how much gift wrap does she need to completely coverthe box?20 cm8 cmOA 1,020 cm²OB. 480 cm²OC. 800 cm²OD. 1,600 cm²

Answer 1

Given:

Regular pentagonal prism with the following dimensions

base edge = 8 cm

height = 20 cm

Recall that the formula for the surface area of a regular pentagonal prism is

$\begin{gathered} SA=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}a^2 \\ \text{where} \\ a\text{ is the base edge} \\ h\text{ is the height} \end{gathered}$

Substitute a = 8 cm, and h = 20 cm. We get

$\begin{gathered} SA=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}a^2 \\ SA=5(8\text{ cm})(20\text{ cm})+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}(8\text{ cm})^2 \\ SA=800\text{ cm}^2+\frac{1}{2}\sqrt{(25+10\sqrt{5})}(64\text{ cm}^2) \\ SA=1020.221107\text{ cm}^2 \end{gathered}$

Rounding to the nearest whole number, Christi needs 1020 cm² of gift wrap.