2018 AIME II Problem 12

Let ABCD be a convex quadrilateral with AB = CD = 10, BC = 14, and AD = 2\sqrt{65}. Assume that the diagonals of ABCD intersect at point P, and that the sum of the areas of triangles APB and CPD equals the sum of the areas of triangles BPC and APD. Find the area of quadrilateral 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.