Question

Find the area of the shaded portion. Show all work for full credit.

Answer 1

Alright, so first of all, you need to find the area of the circle that is part of the cone-shaped area so you can remove it. You need the formula:
 $Area = \pi r^{2} ( \frac{c}{360} )$where c = angle.

Now plug in the answers, and you get:
$A = \pi 6^{2} ( \frac{120}{360} )$.

This would then equal to $12 \pi$.


now, essentially, the shape of this ENTIRE area is of 2 right triangles. Divide 120 by 2, you get 60 degrees. You have 2 60/30/90 triangles (shown in the bottom)


Now, what you need to do is to find the area of the entire thing by using the formula to calculate the right triangle area (A = (1/2)bh). You have b, which is 6. To find the h, you use tan(60) = x/6, which gives you $6 \sqrt{3}$.

The area of one right triangle of this size would be = $18 \sqrt{3}$

Because 2 right triangles, multiply the area by 2 and get: $36 \sqrt{3}$

Now, remember the area of that circle in that total area? subtract it from the total area ($36 \sqrt{3}$) by 12pi and you get 24.65.

The final answer is 24.65

Answer 2

24.65 is your answer to your question. 
I hope this helps!