When you draw three circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r?

assuming the radius is 4 if you join three lines of the circle you find that they are all equal and equal lateral triangle is 60-60-60 all sides are equal using pythagreus you can easily obtain the height 8^2-16 this square root would be 6.9282 the height and base is 8 so the area is 27.7128 of the triangle notice that the that the area of the circle is 50.24 divide by 6(60 degrees is 1/6 of the circle) you will get 8.373333 and multiply by 3 for the 3 parts 25.12 the difference(27.7128-25.12) of 2.5928