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It is sqrt(3) times length of an edge. How to figure. The diagonal across one face is sqrt(2) * edge [make a right triangle: the hypotenuse will be that diagonal].
Now make another right triangle, with the diagonal across the face as one 'leg', and an edge as the other 'leg'. The hypotenuse of this triangle will be a diagonal of the cube: Length of this = sqrt((leg1)2 + (leg2)2) = sqrt((edge)2 + (sqrt(2)*edge)2) = sqrt(edge2 + 2*(edge)2) = sqrt(3*(edge)2) = sqrt(3)*(edge)
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∙ 13y ago
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