2022 AIME II Problem 11

Let ABCD be a convex quadrilateral with AB=2, AD=7, and CD=3 such that the bisectors of acute angles \angle{DAB} and \angle{ADC} intersect at the midpoint of \overline{BC}. Find the square of the area of ABCD.

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.