Circle Area Demonstration/Lab

This is a great proof of the circle area formula with no calculus necessary.

The circular dish holds 10 equal wedges. The parallelogram rearranges the wedges into an orientation that is starting to look rectangular.

The point of the lab is for the kids to see that if you divide the circle into enough wedges, you can arrange them into a rectangle whose height is equal to the radius of the circle, and whose width is equal to pi x radius (half the circumference). From the rectangle area formula, we can then see that the area of a circle is pi times radius^2.

I made one of these for my kids. For a real math lesson, it would be nice to have 3-4 different versions with the same size circle broken into 4, 10, 20 pieces. That would make it clear that with enough pieces, the wedges can be arranged into a rectangle. You could also print wedges on card stock and have the kids cut it out so you don't have to print all the wedges.

The pieces were a tight fit in my templates, but fi