Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.

Correct result:

V =  8235.598 cm³
S =  2517.207 cm²

Solution:

$$\begin{gathered} c=28.6\text{ cm } \\ A=50{}^{\circ } \\ \tan A=c:u \\ u=c\mathrm{/}\tan A^{\circ }=c\mathrm{/}\tan 50^{\circ }=28.6\mathrm{/}\tan 50^{\circ }=28.6\mathrm{/}1.191754=23.99825 \\ a=u\mathrm{/}\sqrt{2}=23.9982\mathrm{/}\sqrt{2}\doteq 16.9693\text{ cm } \\ {S}_1=a^2=16.9693^2\doteq 287.958{\text{cm}}^2 \\ V=S_1\cdot c=287.958\cdot 28.6=8235.598{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_1+4\cdot a\cdot c=2\cdot 287.958+4\cdot 16.9693\cdot 28.6=2517.207{\text{cm}}^2$

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