Ancient babylonian geometry

Question

An old Babylonian tablet calls for finding the area of an isosceles trapezoid whose sides are 30 units long and whose bases are 14 and 50.

Answer 1

That Babylonian method is at least as easy to understand as the standard formula.

                          E___________  
                         /|          |\  
                        / |          | \  
                       /  |          |  \  
                      /   |          |   \  
                     /____|__________|____\  
                     A    B          C    D

The sketch above is not to scale, but it’s good enough to show the idea. You know that the distance $|AD|=50$, that $|BC|=14$, and that $|AB|=|CD|$, so you can calculate $|AB|$. You know that $\triangle ABE$ is a right triangle, and once you’ve calculated $|AB|$, you’ll know both $|AE|$ and $|AB|$ and will be able to use the Pythagorean theorem to calculate $|BE|$. With that information calculating the areas of the central rectangle and the two triangles is easy.