2021 AIME I Problem 9

Let ABCD be an isosceles trapezoid with AD=BC and AB<CD. Suppose that the distances from A to the lines BC,CD, and BD are 15,18, and 10, respectively. Let K be the area of ABCD. Find \sqrt2 \cdot K.

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.