Area of Circle — Formula Derivation (Proof), Example

In this video we derive the formula for the area of a circle. To derive it, we use the formula for the circumference (perimeter) of a circle. We show that the area of a circle is equal to the area of a rectangle whose one side is equal to the radius of the circle and the other side is equal to one half of the circumference. In the end, we use the formula for the area of a circle in an example.

Timestamps:

00:00 - Intro
00:13 - Circumference of a Circle
00:41 - Dividing Circle into Parts
01:30 - Various Numbers of Parts
01:47 - Formula for the Area of a Circle
02:28 - Example
03:58 - Bonus Problem

Image credit (Thumbs Up):

[ohboy]

Simlple, clear, An explanation a kid of 10 years can understand, Bravo !

[neuralwarp]

Great stuff. Another way to prove it is by a summation of circular annuli.

[captainamericawhyso]

But it isn't exactly a rectangle...right?