Constructing A Square From A Pentagon

The
Constructing A Square From A Pentagon
Problem

Given: the pentagon in the figure above, construct a square
whose area equals the area of the given Pentagon.

First, every pentagon can be converted into a collection of triangles whose total area is equal to the area of the given pentagon.

Pentagon To Triangles

            And then, the triangles can be converted to rectangles whose total area is equal to the total area of the triangles, as in problem 2b.
            Next, the rectangles can be converted into squares as in problem 2a.
            Finally, since a square can be constructed from two squares so that the sum of the areas of the two squares equals
            the area of the constructed square (problem 2), then you can do the same with 3 squares, 4 squares, 5 squares,
            and so on, with as many squares as needed. Why is that?

Return to the previous page: ® 'Not So Familiar' Pythagorean Implications
Pythagoras.html