# Math Help - Shaded area

I was discussing this question with my friends but we're all disagreeing...

Here's what I started with:
If you draw bisectors from each of the vertices of the inner triangle (enclosing circle with r), the vertical line will be split into a 2:1 ratio, which is 2r:r
Is this the right way to start?

I would start by calculating the area of the inner triangle. It's height is 2R (as you note it's 2R from the center to the top vertice, plus 1r from the center to the base), and its base is $2 r \sqrt 3$ - do you see why that is? Next find the radius of the larger circle - oh wait, we've already determined that it's 2R - and determine its area. Finally find the height and base of the large triangle so you can determine its area. Then the shaded area is:
$Area = A_{Large\ T} - A_{Large \ C} + A_{Small\ T} - A_{Small \ C}$