Given Data:
The radius of the circle is, r = 4
The angle is, 98.
The measure of angle that an arc makes at the center of the circle of which it is a part. Therefore, the measure of the arc AB is 90.
The length of the arc AB can be calculated as,
[tex]\begin{gathered} L=\frac{98}{360}\times2\times\pi\times r \\ \text{ =}\frac{98}{360}\times2\times3.14\times4 \\ \text{ =}6.84 \end{gathered}[/tex]
The area of the shaded section is equal to the area of the arc, which can be calculated as,
[tex]\begin{gathered} A=\frac{98}{360}\times\pi\times r^2 \\ \text{ =}\frac{98}{360}\times3.14\times4^2 \\ \text{ =}13.67 \end{gathered}[/tex]
The area of the unshaded region can be calculated by subtracting the area of the arc from the area of the total circle. The area of the total circle is,
[tex]A^{\prime}=\pi\times r^2=3.14\times4^2=50.24[/tex]
Therefore the area of the unshaded region can be calculated as,
[tex]A=50.24-13.67=36.57[/tex]
