2018 AIME II Problem 12


Let ABCDABCD be a convex quadrilateral with AB=CD=10AB=CD=10, BC=14BC=14, and AD=265AD=2\sqrt{65}. Assume that the diagonals of ABCDABCD intersect at point PP, and that the sum of the areas of APB\triangle APB and CPD\triangle CPD equals the sum of the areas of BPC\triangle BPC and APD\triangle APD. Find the area of quadrilateral ABCDABCD.


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.

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Category: AIME II
Points: 5
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