A really big cake

by mathgrant

Having completed your first exam without needing so much as a potty break, you're feeling pretty confident. Your next exam is scheduled in, of all places, the school cafeteria.

You arrive at the cafeteria early and sit down in your favourite corner. There is a very very large cake on a table in the center of the room. Within a minute, Dr. Grant strolls in. "Ah, good," he says. "Tell me the area of the top of this massive cake." (don't worry about the sides)

With your trusty yardstick, you measure the sides of the cake. The sides are, in order, 8, 15, 10, and 18 feet long.

Dr. Grant smiles and tells you the following:

If you labeled the corners of the cake C, A, K, and E in order, then angles C + A = K + E

You sit down and draw a sketch. It seems like there should be a solution...

See the Solution