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°:
[tex]A_{ABC}=\frac{60}{360}*\pi *r^{2}\\A_{ABC}=\frac{60}{360}*\pi *(6\sqrt{3})^{2}\\A_{ABC}=56.54[/tex]
Now calculate the the area of the white triangle in the wedge, by using a base length of [tex]3\sqrt{2}[/tex], and height:
[tex]h=\sqrt{(6\sqrt{3})^{2}-(3\sqrt{3})^{2}} \\h=9[/tex]
[tex]A_{TRI}=\frac{1}{2}*9*6\sqrt{3} \\A_{TRI}=27\sqrt{3} \\A_{TRI}=46.78[/tex]
Find the area of the red segment:
[tex]A_{ABC} -A_{TRI}\\=56.54-46.78\\=9.76[/tex]
