2024 SSMO Accuracy Round Problems/Problem 5

Problem

Let $ABCD$ be a convex quadrilateral such that $\angle ABC = 120^\circ$ and $\angle ADC = 60^\circ$ . If $AB = BC = CD = 5$ , the area of $ABCD$ can be expressed as $a+b\sqrt{c},$ where $a,b,$ and $c$ are positive integers and $c$ is squarefree. Find $a+b+c.$

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2024 SSMO Accuracy Round Problems/Problem 5

Problem

Solution