Quadrilateral prism

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

Correct answer:

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

Step-by-step explanation:

v=10 cm θ=60 ∘  tan θ = v:u  u=v/tanθ=v/tan60° =10/tan60° =10/1.732051=5.7735 cm  u = 2​ a  a=u/2​=5.7735/2​=4.0825 cm
S1​=a2=4.08252=350​≐16.6667 cm2 S2​=4⋅ a⋅ v=4⋅ 4.0825⋅ 10≐163.2993 cm2  S=2⋅ S1​+S2​=2⋅ 16.6667+163.2993=196.6326 cm2
V=S1​⋅ v=16.6667⋅ 10=166.6667 cm3

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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