Hexagonal prism

Calculate the volume and surface of a regular hexagonal prism with the edge of the base a = 6 cm with the corresponding height v1 = 5.2cm and the height of the prism h = 1 dm.

Correct answer:

V =  936 cm³
S =  547.2 cm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ {v}_1=5.2\text{cm} \\ h=1\text{dm}\to \text{cm}=1\cdot 10\text{cm}=10\text{cm} \\ n=6 \\ {S}_1=\frac{a\cdot v_1}{2}=\frac{6\cdot 5.2}{2}=\frac{78}{5}=15.6{\text{cm}}^2 \\ {S}_6=n\cdot S_1=6\cdot \frac{78}{5}=\frac{6\cdot 78}{5}=\frac{468}{5}=93.6{\text{cm}}^2 \\ V=S_6\cdot h=\frac{468}{5}\cdot 10=\frac{468\cdot 10}{5}=\frac{4680}{5}=936{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_6+n\cdot a\cdot h=2\cdot \frac{468}{5}+6\cdot 6\cdot 10=547.2{\text{cm}}^2$

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