Suppose you want to find the area of a dodecagon inscribed in a circle of radius 1. One way to do this is to divide the dodecagon into 12 isosceles triangles with two sides of length 1 and an angle between them of 30°. Then we can use the formula for the area of a triangle
There’s another way to get this result which doesn’t rely on knowing that
Move the slider, or click the play button to start the animation. There’s a little bit of thinking to be done to convince yourself that the pieces fit nicely together with no gaps, but I hope you agree it’s a very pleasing way to show that the area of the dodecagon is 3 square units!