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<ABC +<BCD = 270^o, |AB| = 8, |BC| = 29, |CD| = 24 ,|DA| = 53

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

January 7, 2022
anglesgeometry

Problem Statement

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