If three sides of trapezoid are each 6 inches long, how long must the fourth side be if the area is maximum?

A trapezoid can be seen as a rectangle with a triangle split in half. the largest area that a triangle can make with two sides of 6 would be a right triangle, which means that the last side is 6 * square root of 2.

The rectangle will have two sides of size 6 guaranteed. therefore, the last side would be a side of length 6+6*sqrt 2