Question

Find the area of the shaded segment of the circle . The area of the shaded segment is _M2(Round to the nearest tenth as needed .)

Answer 1

Given data:

The given figure.

The major arc angle is 300 degree, it means the minor arc angle is 60 degree, so the triangle inscribed in the circle is equilateral triangle.

The expression for the area of the shaded region is,

$\begin{gathered} A=\frac{60^{\circ}}{360^{\circ}}(\pi)(7)^2-\frac{\sqrt[]{3}}{4}(7)^2^{} \\ =\frac{1}{6}(\pi)(7)^2-\frac{\sqrt[]{3}}{4}(7)^2 \\ =25.65-21.22 \\ =4.43 \end{gathered}$

Thus, the area of the shaded region 4.43 sq-units.