Why is the area of a circle πr2?

Why is the area of a circle πr2?

The height becomes equal to the radius, while the length is half of the circumference (C = 2πR) which now finds itself running along the top and bottom. As the number of triangles “approaches infinity” the circle can be taken apart and rearranged to fit almost perfectly into an “R by πR” box with an area of πR2.