Major Update: Solution to last night's geometry problem.

Here is the solution:

Make X = to the radius of the circle.
Then add up all the pieces that make up the perimeter of the trapezoid (starting at the upper left and working around clockwise):

Perimeter = X + (16-X) + (16-X) + (7-X) + (7-X) + X + X + X

Perimeter = 46