Question

In the figure below, the circle is inscribed in the equilateral triangle. If the diameter of the circle is 2, what is the sum of the shaded area?
(a) 3 square root 3 - pi
(b) 3 square root 3 - 4pi
(c) 3 square root 3 - (3pi)/2
(d) 6 square root 3 - (3pi)/2
(e) 108 - pi

Answer 1

ugh.
I've worked this problem at least 3 times today.
If you look at the geometry you will be able to show that the area of this triangle is
3 sqrt(3). Given that the radius = 1.

Answer 2

wait how do you know that the area's 3 sqrt(3)

Answer 3

draw two altitudes in the triangle

Answer 4

notice that the small triangle that they form is a 30-60-90 tirangle.

Answer 5

i see