Which takes up more space:
A single circle inscribed in a triangle, touching each side at a single point? Or, four identical circles, with 3 of them touching the center circle, and those same 3 touching one point each on the three sides of the triangle?????
at least in the case of an equilateral triangle, a little diagramming should convince you that the small circles have 1/2 the radius of the larger circle. So, the sum of their areas is the same as the area of the large circle.
Not sure about other triangles, though ...