Congruent Cake Slices

Here's a plan (top down view) of a cake. The challenge is to cut the cake into congruent pieces. Two and three pieces are pretty easy and may serve as a nice warm up, but then four becomes more challenging.

Here's a solution. There may be others.

An interesting finding while trying to solve the problem is below. This cuts the cake into four pieces of equal size, but they are not congruent. One of my students did, however, point out that it looks 3 dimensional - four congruent rectangles arranged in an L shape - which I thought was a clever loophole of sorts.