Question

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

the quadrilateral inside the circle is a square.

Short answer

The area of the blue shaded region in the given figure is 41.04

Step-by-step solution

Step 1. Given information

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

Step 2. Find radius and diameter

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

Step3. Finding the area of a square

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$$\begin{gathered} A=\frac{d^2}{2},d=diagonal \\ =\frac{{12}^2}{2} \\ =\frac{144}{2} \\ =72 \end{gathered}$$

Step 4. Finding the area of a circle

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

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

Step 5. Find the area of the blue shaded region

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

Then according to the given figure

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