The locus of a point is such that the distance from a fixed point to its circumference is always constant. The fixed point is called the centre of the circle. The area of the circle is [tex]36 \pi\;\rm{unit^2}[/tex] and the area of the section is 22.26 squared units.
The radius of the circle is given is 6 units.
The formula for finding the area of the circle is given as [tex]\pi r^2[/tex].
Thus,
[tex]\rm{Area}= \pi (6)^2\\=36 \pi[/tex]
Now, we have to find the area of the shaded portion that is given in the figure.
Area of shaded portion = Area of the minor sector ABC - Area of triangle CDE
Therefore,
The triangle CDE is a right triangle that is ordered pair of 3,4,5.
Thus, the angle subtends by sector at the center of the circle is 90 degrees.
Therefore,
[tex]\begin{aligned} \rm{Area \;of\; sector}&=\dfrac{\pi r^2 \theta}{360}\\&=\dfrac{\pi \times 36\times 90}{360}\\&=9 \pi\\&=28.26 \end{aligned}[/tex]
[tex]\begin{aligned} \rm{Area \;of\;triangle}&=\dfrac{1}{2} \times CD \times CE\\&=\dfrac{1}{2} \times 3 \times 4\\&= 6 \end{aligned}[/tex]
Hence,
Area of shaded portion = Area of the minor sector ABC - Area of triangle CDE
Area of shaded portion = 28.26 - 6 = 22.26.
To know more about the area of sector, please refer to the link:
https://brainly.com/question/12564650
