The space diagonal of a rectangular prism is the square root of l² + w² + h². A 3-by-4-by-12 box has diagonal 13. Solids as a set are in solid geometry.
Two Pythagorean steps
First find a face diagonal, then use that with the third edge. Or square all three edges at once. Face diagonals are ordinary Pythagorean, in Pythagorean theorem and special right triangles.
Volume of the same box is lwh, in area and volume. Surface area counts the faces, in surface area.
The bottom line
Square length, width, and height. Add. Square-root. That is the space diagonal.
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