Question

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1. Find the volume of the parallelepiped with the vertices in the given order: (0, 0, 0), (3, 0, 0), (0, 5, 1), (2, 0 , 5), (3, 5, 1), (5, 0, 5), (2, 5, 6), and (5, 5, 6). Sketch the solid.

Answer 1

Volume(since this is the parallelepiped) = abc, where

a = distance((5,0,5), (2,0,5)) = 3

b = distance ((2,0,5), (2,5,6)) = $\sqrt{\smash[b]{(2-2)^2 + (0 - 5)^2 + (5 - 6)^2}} = \sqrt{\smash[b]{26}}$

c = distance ((5,0,5), (3,0,0)) = $= \sqrt{\smash[b]{(5 -3 )^2 + (0 - 0)^2 + (5 - 0)^2}} = \sqrt{\smash[b]{29}}$

V = abc = $3\sqrt{\smash[b]{754}}$