Area of a Circle from Dissections
This applet will help you see the relationship between the area of a circle and its circumference.
What happens when you move the slider to dissect the circle into more parts? Would you want to dissect the circle into more or fewer parts? Why? Now, unroll the circle using the check box. Use the formula for the area of a triangle to try to find the area of the triangle. What is the area of that triangle? (this should be a formula). Now use the 2nd slider to change the triangle to a rectangle. What is the area of that rectangle? (this should be a formula) How does the area of that rectangle compare to the area of that triangle from the previous step? From all of this, what do you think the formula for the area of a circle is?