Find the area of the blue shaded region in the figure, assuming

the quadrilateral inside the circle is a square.

A square inside the circle is given and Some parts of the regions are shaded.

We have to find out the area of that shaded region

According to the given information equation of the given circle is $x^2+y^2=36$and it is the in the form of standard equation of a circle at origin (0,0) and radius r $x^2+y^2=r^2$

Hence radius is 6 and diagonal is 12 since the diameter is 2times of radius

Here radius is 6 and diagonal is 12.We know that diameter of the circle is the diagonal of a square , thus diagonal of a square is 12

Thus area of a square is$$\begin{gathered} A=\frac{d^2}{2},d=diagonal \\ =\frac{{12}^2}{2} \\ =\frac{144}{2} \\ =72 \end{gathered}$$

In the given circle radius r =6 , then area of circle

$$\begin{gathered} A=\pi \times r^2 \\ =3.14\times 36r=6 \\ =113.04 \end{gathered}$$

The area of the circle here is 113.04 and the area of the square is 72.

Then according to the given figure

$$\begin{gathered} areaofablueshadedregion=areaofthecircle-areaofthesquare \\ =113.04-72 \\ =41.04 \end{gathered}$$