We know that the area of a circle is: A=πr². But a real proof of this is hard.
Here we show a demonstration of this fact by cutting the circle into wedges and placing half of the wedges face up and half face down. As the number of wedges increases, we see that they cover a rectangle with A=base•height = ½ of circumference •radius = ½(2πr)•r = πr²

Why is the base of the rectangle half of the circumference of the circle?
Why did we label the x-axis with units of π and the y-axis with units of numbers?