Answer:
[tex]6\pi-9\sqrt{3[/tex]
Step-by-step explanation:
The area of a pie-slice shape can be found with the equation [tex]A=\pi nr^2/360[/tex] where n is the angle of the shape and r is the radius of the circle. In this case, n=60 and r=6. Therefore, the total area of the pie-slice is [tex]\pi (60)(6^2)/360=6 \pi[/tex]
Next, the triangle that makes up the unshaded part of the segment is an equilateral triangle because the angle is 60. The area of an equilateral triangle is [tex]\sqrt{3}r^2/4[/tex] where r is the length of one of its side (in this case, r=6). Plugging that in, we get an area of [tex]9 \sqrt{3}[/tex]
Finally, the area of the shaded is the area of the pie-slice minus the area of the triangle: [tex]6\pi-9\sqrt{3[/tex]
