Triangular prism,

The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l).

Correct result:

V =  7180.4472 cm3

Solution:

S=2514 cm2 S1=3/4 a2  S=2⋅ S1+3a⋅ a  S=3/2 a2+3a2 S=(3/2+3)a2  a=S3/2+3=25143/2+3≐25.5006 cm  S1=3/4⋅ a2=3/4⋅ 25.50062≐281.5796   V=S1⋅ a=281.5796⋅ 25.5006≐7180.4472=7180.4472 cm3   Verifying Solution:  S2=2⋅ S1+3⋅ a2=2⋅ 281.5796+3⋅ 25.50062=2514 cm2 S2=S

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