Question

HELP!!! 20 POINT REWARD!!!

Answer 1

Ah! I love these questions!

To find the area of the shaded region, you must find the area of the circle. Then, you must find the area of the triangle inscribed in the circle. Lastly, you must subtract the area of the triangle from the area of the circle.

Area of Circle: $\pi$ x $r^{2}$
=$\pi$ x 10^2
=$\pi$ x 100
Usually these problems will not require you to convert pi into a decimal, but if it does, then the area of the circle would be 314. 

Area of Equilateral Triangle: $\frac{ s^{2} \sqrt{3} }{4}$
To find the side, draw a perpendicular line from the center to a side of a triangle. This line will create two more triangles inside the big triangle. You will notice how in these smaller triangles, the angles are 30, 60, 90. From that we can deduce that half the length of a side is 5$\sqrt{3}$ because of the 30, 60, 90 ratio. Multiply that by 2 to get 10$\sqrt{3}$ as the length of the side of the large triangle. Now substitute this value into the formula above.
$\frac{ (10 \sqrt{3}) ^{2} x \sqrt{3} }{4} = \frac{300 \sqrt{3} }{4} = 75 \sqrt{3}$

Final Answer: 100$\pi$ - 75$\sqrt{3}$