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adelina 88 [10]
3 years ago
5

What is the area of the shaded segment?

Mathematics
1 answer:
Whitepunk [10]3 years ago
8 0

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

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