Triangular prism

The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C', has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.

Correct result:

V =  65.45 cm³

Solution:

$$\begin{gathered} a=6cm \\ {h}_1={\displaystyle \frac{\sqrt{3}}{2}}a=5.196cm \\ \tan 22^{\circ }={\displaystyle \frac{h\mathrm{/}2}{h_1}} \\ h=2h_1\tan 22^{\circ }=2\cdot 5.196\cdot \tan 22^{\circ }=4.199cm \\ {S}_1={\displaystyle \frac{1}{2}}a{h}_1={\displaystyle \frac{1}{2}}6\cdot 5.196=15.588c{m}^2 \\ V=S_{1}h=15.588\cdot 4.199=65.45{\text{cm}}^3 \end{gathered}$$

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