2015 AIME I Problem 4

Point B lies on line segment \overline{AC} with AB=16 and BC=4. Points D and E lie on the same side of line AC forming equilateral triangles \triangle ABD and \triangle BCE. Let M be the midpoint of \overline{AE}, and N be the midpoint of \overline{CD}. The area of \triangle BMN is x. Find x^2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.