Area of a Circle by Lines

Have a look at this:

A circle becomes a triangle! And the area is:

Conclusion:

Area of Circle = πr²

Also notice:

Things to Try

Try a low value for "sides":

• you can see that the lengths don't change as they unfold into straight line segments
• also notice they are actually polygons, which head towards being circles as the number of sides increase

Also try increasing the value of "lines" to convince yourself that the lines are heading towards filling the whole area.