Proof that the area of a circle is πr2 (without math)
Why is the area of a circle equal to Pi times the radius squared?
Pi (π) is defined as the circumference of a circle divided by the diameter of the circle.
Pi is also how many times the diameter fits around the
circumference (3.14159... times). Since the radius is equal to half the diameter,
Pi can also be defined as the number of times the radius fits
around the outside arch of a half circle. The length of the arch of a half circle is therefore π times
the radius of the circle (πr in the figures below).
FIGURE 1: πr is the length of a half circle.
The figure below shows how the circle can be cut up in pieces and rearranged to approximate
a rectangle with one side equal to the radius, r, and the other side equal to πr.
The rectangle becomes closer to perfect as the slices are made thinner.
