see the attached figure to better understand the problem
we know that
the area of a square is equal to
\(A=b^{2}\)
where
b is the length side of the square
in this problem, the length side of the square is equal to the diameter of the circle
so
b=2r
substitute in the formula of the area of the square
\(A=(2r)^{2}\)
\(A=4r^{2}\ units^{2}\)
Find the area of the circle
the area of the circle is equal to
\(A=\pi r^{2}\ units^{2}\)
Find the area of the grass
the area of the grass is the area of the square minus the area of the circle
so
\(A=4r^{2} - \pi r^{2} = r^{2}*[4-\pi ]\)
therefore
the answer is
the area A of the grass as a function of r is equal to
\(A=r^{2}*[4-\pi ]\ units^{2}\)
