Question

50 POINTS!!! Find the area of the segment of circle C shown in the diagram above.

Answer 1

Answer:

B. 9.76 u²

Step-by-step explanation:

First calculate the area of the 60° wedge of the circle by calculating the area of the full circle and multiplying it by a fraction of 60°/360°:

$A_{ABC}=\frac{60}{360}*\pi *r^{2}\\A_{ABC}=\frac{60}{360}*\pi *(6\sqrt{3})^{2}\\A_{ABC}=56.54$

Now calculate the the area of the white triangle in the wedge, by using a base length of $3\sqrt{2}$, and height:

$h=\sqrt{(6\sqrt{3})^{2}-(3\sqrt{3})^{2}} \\h=9$

$A_{TRI}=\frac{1}{2}*9*6\sqrt{3} \\A_{TRI}=27\sqrt{3} \\A_{TRI}=46.78$

Find the area of the red segment:

$A_{ABC} -A_{TRI}\\=56.54-46.78\\=9.76$

Answer 2

• B.the area =9.76u^2
• the area of the sector =1/2 x r^2 x (the angle in radian -sin(the same angle in degrees)