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 result:

V =  936 cm³
S =  547.2 cm²

Solution:

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

$S=2\cdot S_6+n\cdot a\cdot h=2\cdot 93.6+6\cdot 6\cdot 10={\displaystyle \frac{2736}{5}}={\displaystyle \frac{2736}{5}}{\text{cm}}^2=547.2{\text{cm}}^2$

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