Here is a wonderful problem I read about in Sanjoy Mahajan’s Street-Fighting Mathematics (link to full book pdf).
Suppose you have an equilateral triangle and you want to cut it in half using a pizza cutter (which can cut curves, not just straight lines). What is the shortest cut you can make?
“Cut in half” means you wind up with two pieces of equal area, not necessarily two identical pieces.
Hint: You might be able to solve this with some fancy calculus, but you can get away with a picture if it’s clever enough.