Farmer John has a large field of soybeans. There are three months left until har

Question

Farmer John has a large field of soybeans. There are three months left until harvest time, and the almanac has forecast a very dry summer. His old irrigation system sprays too much water past the soybean crops, so he is thinking about installing a more efficient circular irrigation system. As he considers the cost of the new system, the cost of irrigation water, the going price of soybeans, and the irrigated and unirrigated areas, he sketches a map of his soybean field that shows how the irrigation system would cover the crops:

You have to solve two problems for this project:The square ABCD has its 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 its area is.

Draw an image that looks like the image above.

Compute the area of the shaded region, given the the length of one of the sides of the square ABCD as user input. Your answer should be accurate to two decimal places.

This is in python

Explanation / Answer

Here is the code in Python

Area of the shaded area = Area of the square - Area of one full circle

The diameter of the circle is equal to the length of the square side

Radius = Diameter/2

----------------------------------------------------------------------------------------------------------------

import math

def compute_area(len):
  
square_area =len**2
radius=len/2
area_of_the_circle = math.pi * radius * radius
return round(square_area-area_of_the_circle,2)

print(compute_area(14))

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