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2024 SSMO Accuracy Round Problems/Problem 5

Revision as of 15:42, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>ABCD</math> be a convex quadrilateral such that <math>\angle ABC = 120^\circ</math> and <math>\angle ADC = 60^\circ</math>. If <math>AB = BC = CD = 5</m...")
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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 $a+b+c.$

Solution

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