Method of exhaustion

Imagine you have a big piece of cake that you want to measure. You don't have a ruler, but you do have a smaller piece of cake that you know the size of.

So you start by cutting the big piece of cake into smaller and smaller pieces until they're the same size as the smaller piece you know the size of. Then you count how many of those smaller pieces fit into the big piece. And from that, you can figure out how big the big piece of cake is!

This is basically how the method of exhaustion works. Instead of cake, though, it's used to figure out things like the area and circumference of a circle. You take a shape, like a circle, and divide it into smaller and smaller shapes (like triangles or rectangles) whose areas you can calculate. By adding up all those areas, you can get closer and closer to the area of the circle you started with.

It's kind of like counting how many pieces of cake fit into the big piece, but instead of counting, you're adding up all the smaller areas. And just like with the cake, the more smaller shapes you use, the more accurate your final answer will be!