Problem

Source: 2020 Dürer Math Competition Finals Day2 E11 https://artofproblemsolving.com/community/c1622639_2020_

Tags: angles, geometry



The convex quadrilateral $ABCD$ has $|AB| = 8$, $|BC| = 29$, $|CD| = 24$ and $|DA| = 53$. What is the area of the quadrilateral if $\angle ABC + \angle BCD = 270^o$?