A Hexagon and a Triangle in a Circle

A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 10 units. What is the area of the region between the two polygons?

Make sure you explain your answer - answers that include just a number will not be considered correct! I know the answer already - what I want to know is how you figured it out.