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C - 48P
The height of the triangle equals \(6\sqrt{3}\) since the sides are 6 and 12 (1:2: \sqrt{3} ratio). So the area of the triangle is \((6\sqrt{3}*12)/2=36\sqrt{3}\)
Since the triangle is equilateral, we can get 3 equal triangles with area of each \(36\sqrt{3}/2=12\sqrt{3}\). From this we can get the heights of the smaller triangles: \(12\sqrt{3}*2/12=2\sqrt{3}\). Thus, the radius is \(6\sqrt{3}-2\sqrt{3}=4\sqrt{3}\). The area of the cirle is \((2\sqrt{3})^2*P=48P\)