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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?A 800 cm²B. 480 cm2C. 1,020 cm²D. 1,600 cm²

Select the correct answerChristi is using a display box shaped like a regular pentagonal prism as a gift box About how much gift wrap does she need to completel class=

Respuesta :

Given: A regular pentagonal prism with base edge 8cm and height 20 cm .

Find: wrap need to cover the box.

Explanation: for to find the length of wrap we need to find the area of regular pentagonal prism .

[tex]A=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5)}}a^2[/tex]

where a=base edge=8cm and h =height=20 cm

[tex]\begin{gathered} A=5\times8\times20+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}\times8^2 \\ =1020.2211\text{ cm}^2 \end{gathered}[/tex]

Final answer: the required answer is 1020 square centimeter.

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