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

1020 cm²

Explanation:

Answer 2

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+(1)/(2)\sqrt{5(5+2√(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+(1)/(2)\sqrt{5(5+2√(5))}a^2 \\ SA=5(8\text{ cm})(20\text{ cm})+(1)/(2)\sqrt{5(5+2√(5))}(8\text{ cm})^2 \\ SA=800\text{ cm}^2+(1)/(2)\sqrt{(25+10√(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.