​Pythagorean Theorem and Rectangular Solids

About Geometry Worksheet Assignment 7.6:     

 

Assignment 7.6 is an introduction to the use of the Pythagorean Theorem in calculating the lengths of diagonals in rectangular solids.

 

Prerequisite Skills:  Apply the Pythagorean Theorem to find lengths of sides in right triangles (Assignment 7.3). 

 

Definitions:  A rectangular solid is a closed three-dimensional figure of six rectangles.   

                           A diagonal of a rectangular solid is a line segment that is not a side or diagonal of any of the rectangles with its endpoints at the vertices of

                           non-adjacent rectangles.

 

Theorem:    In a rectangular solid, the sum of the squares of the length, width, and height equals the square of the length of the diagonal of the solid.

                            2        2        2        2

                          d    =  l   +   w   +   h    ( d is diagoanl length; l is length; w is width; h is height)