montargent

The size of a circle is specified by either its radius or its diameter.  All points on a circle are the same distance from its center.  A line sement from the center of a circle to its periphery is called a radius.  The lengths of all radii of a circle are the same.  We often refer to the length of a radius as "the radius."

Any line segment connecting two distinct points on a circle is a chord.

A chord which passes through the center of a circle is a diameter.

The length of any diameter is exactly twice the length of any radius. 

The circumference of a circle has length proportional to the length of a diameter.  The constant of proportionality is "pi".  Thus, C = Pi * D .


The perimeter of a square of side D is 4*D.   The circumference of a circle of diameter D is Pi*D, so
the ratio of the circumference of a circle of diameter D to the perimeter of a square of side D  is Pi/4. 

The area a square of side D   is  D^2.   The area of a circle of diameter D is  (Pi/4)*D^2.
Thus, the ratio of the area of a circle of diameter D to a square of side D is (Pi/4).

Note that the ratio of the CIRCUMFERENCE of the circle to the PERIMETER of the square is the SAME as the ratio of the AREA of the circle to the AREA of the square.  In both cases the ratio is  Pi/4  (approximately 3/4).