#### O. W. Grant

**Registered Senior Member**

given:

a circle, radius = r;

angle of one radian.

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Radian

https://en.wikipedia.org/wiki/Radian

A radian on a circle has sides: a radius, a radius, an arc with length 1 radius.

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(1)

__Area of the circle__= π.r^2

A circle has 2.π. rad.

If

__area of 1 radian angle__=1

**rad**

then

(2)

__area of the circle__= 2.π.

**rad**

(1), (2) => 2.π.

**rad**= π.r^2 <=> 2.

**rad**= r^2

The area of two radians makes (the area of) one square?