Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.

Correct result:

a =  4.0825 cm
S =  196.6326 cm2
V =  166.6667 cm3

Solution:

v=10 cm θ=60  tanθ=v:u  u=v/tanθ=v/tan60 =10/tan60 =10/1.732051=5.7735 cm  u=2a  a=u/2=5.7735/2=4.0825 cm
S1=a2=4.08252=50316.6667 cm2 S2=4 a v=4 4.0825 10163.2993 cm2  S=2 S1+S2=2 16.6667+163.2993=196.6326 cm2
V=S1 v=16.6667 10=5003=166.6667 cm3



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