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2024 AMC 10A Question 22

AMC10 · 2024 AMC 10A

Question 22

Let $\mathcal{K}$ be the kite formed by joining two right triangles with legs $1$ and $\sqrt3$ along a common hypotenuse. Eight copies of $\mathcal{K}$ are used to form the polygon shown below. What is the area of $\triangle ABC?$

Question illustration
  1. $2 + 3\sqrt3$
  2. $\dfrac{9}{2}\sqrt3$
  3. $\dfrac{10 + 8\sqrt3}{3}$
  4. $8$
  5. $5\sqrt3$