Wire model

A wire model of a regular hexagonal prism has a base edge length of a = 8 cm and a height of v = 12 cm. The solid is covered with paper — the bases with dark paper and the lateral surface with white paper.

- Calculate in cm the greatest possible straight-line distance between two vertices of the wire prism (the thickness of the wire is neglected).

- Calculate in cm² the area of the white paper on the lateral surface of the prism.

Final Answer:

u =  20 cm
S =  576 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ v=12\text{cm} \\ {u}^2=v^2+(2a{)}^2 \\ u=\sqrt{v^2+(2a{)}^2}=\sqrt{12^2+(2\cdot 8{)}^2}=20\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=\frac{\sqrt{3}}{4}\cdot a^2{\text{cm}}^2 \\ o=6\cdot a=6\cdot 8=48\text{cm} \\ S=o\cdot v=48\cdot 12=576{\text{cm}}^2 \end{gathered}$$

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