Question

1. The prism below measures 6 inches x 3 inches x 10 inches. A diagonal

Answer 1

9514 1404 393

Answer:

  √145 ≈ 12.04

Step-by-step explanation:

The length of the space diagonal is the root of the sum of the squares of the prism edge lengths:

  d² = a² +b² +c² = 6² +3² +10² = 145

  d = √145 ≈ 12.04 . . . inches

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The face diagonal is found using the Pythagorean theorem in the usual way:

  f² = a² + b²

The space diagonal is the hypotenuse of the right triangle whose sides are the face diagonal and the remaining edge:

  d² = f² +c²

  d² = a² +b² +c²

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Here is a diagram.