Quadrilateral prism

The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body.

Final Answer:

V =  19595.9179 cm³

Step-by-step explanation:

$$\begin{gathered} a=20\text{cm} \\ \alpha =60{}^{\circ } \\ S=a^2=20^2=400{\text{cm}}^2 \\ {u}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 20=20\sqrt{2}\text{cm}\doteq 28.2843\text{cm} \\ c=u_1\cdot \tan \alpha =u_1\cdot \tan 60°=28.2843\cdot \tan 60°=28.2843\cdot 1.732051=48.98979 \\ V=S\cdot c=400\cdot 48.9898=19595.9179{\text{cm}}^3 \end{gathered}$$

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