Farmer John has four fields of soybeans planted. There are three months left until harvest time, and the almanac has forecast a very dry summer. Farmer John has decided to put in a new, more efficient irrigation system to water his soybean crops. His estimate is that the new system will cost about $10,000. Since soybeans are going for about $12.75 a bushel, Farmer John wants to harvest as many bushels of soybeans as he possibly can. As he ponders on this problem, he sketches a map of his soybean fields that shows how the irrigation system will cover the crops. This is shown on the left.

The square ABCD has it's vertices located at the centers of four identical circles, which are the regions covered by the new circular irrigation system. Farmer John is intrigued by the pattern shown in the shaded region of the map, and wonders what the area of this shaded region is.

You have to solve two problems for this project:

Draw an image that has 4 equal circles that are touching but not overlapping. The shaded region is the area between the 4 circles.

Compute the area of this shaded region, given the the length of one of the sides of the square--which can be a real number--as user input. Your answer should be accurate to two decimal places

A D B