So Why PI?
Get yourself a nice piece of paper, a pencil, and an eraser. A ruler would be nice, a compass would be nice. Neither are necessary.

Draw a big circle. Draw a line from top to bottom of the circle. Draw another line at right angles to the first line.

Draw 4 lines outside the circle at right angles to those, touching the circle, so that you have a square just outside the circle, touching it at those 4 points.

From the intersection of the lines inside the circle, put an "r" on each of those 4 lines inside the circle. That is to say, you've indicated each of those lines is of "r" length, also called the "radius."

Look at the 4 squares you've made. Each side is "r" in length.

Soooo, the area of each square is r X r, or r^2 (pronounced "r squared", and not worrying so much that Blogger doesn't like superscripts)

Soooo, the area of the BIG square is 4 X r^2, since the BIG square is composed of 4 small squares of equal area.

IF the circle completely covered the BIG square, the area of the circle would be
4 X r^2. But there are 4 little bits in the corners of the square that aren't covered by the circle.

Soooo, to accomodate those little bits not covered, the area of the circle is
3.1416 X r^2 or PI X r^2, instead of 4 X r^2.

Want to proceed further and physically approximate PI?

Get a BIG circle of something hard, say a table. Use a cloth or plastic tape measure, and measure the CIRCUMFERENCE of the circle, being very careful to write down the results including the fraction part.

Find the center of the circle. Measure the DIAMETER of it carefully.

Either using long division or a calculator, divide the DIAMETER into the CIRCUMFERENCE. You should have a pretty good approximation of PI.