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The diagonal of a right rectangular prism is the line that connect opposite vertices. In other word is the distance from corner to corner in the right rectangular prism. Since the diagonal of a right rectangular prism is the hypotenuse of a right triangle, we are going to use a variation of the Pythagorean theorem to find it. In essence, we just need to add another dimension to the Pythagorean theorem; in this case the height of our prism:
We can conclude that the formula to calculate the length of the diagonal of a right rectangular prism is:
where
is the length of the diagonal.
is the length of the rectangular base of the prism.
is the width of the rectangular base of the prism.
is the height of the prism.
We can conclude that the formula to calculate the length of the diagonal of a right rectangular prism is:
where