Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.

Correct result:

V =  8235.5985 cm³
S =  2517.2067 cm²

Solution:

$$\begin{gathered} c=28.6 \\ A=50\pi \mathrm{/}180=50\cdot 3.1416\mathrm{/}180\doteq 0.8727 \\ {u}_2=c\mathrm{/}\tan (A)=28.6\mathrm{/}\tan (0.8727)\doteq 23.9982 \\ a=u_2\mathrm{/}\sqrt{2}=23.9982\mathrm{/}\sqrt{2}\doteq 16.9693 \\ {S}_1=a^2=16.9693^2\doteq 287.958 \\ V=S_1\cdot c=287.958\cdot 28.6=8235.5985{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_1+c\cdot 4\cdot a=2\cdot 287.958+28.6\cdot 4\cdot 16.9693=2517.2067{\text{cm}}^2$

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