Question

What is the area of the shaded segment?

Answer 1

Answer:

$6\pi-9\sqrt{3$

Step-by-step explanation:

The area of a pie-slice shape can be found with the equation $A=\pi nr^2/360$ 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 $\pi (60)(6^2)/360=6 \pi$

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 $\sqrt{3}r^2/4$ where r is the length of one of its side (in this case, r=6). Plugging that in, we get an area of $9 \sqrt{3}$

Finally, the area of the shaded is the area of the pie-slice minus the area of the triangle: $6\pi-9\sqrt{3$