Problem 96

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Problem 96: (2024 AMC 10a, 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 $\Delta ABC$? $\textbf{(A) }2+3\sqrt3\qquad$ $\textbf{(B) }\dfrac92\sqrt3\qquad$ $\textbf{(C) }\dfrac{10+8\sqrt3}{3}\qquad$ $\textbf{(D) }8\qquad$ $\textbf{(E) }5\sqrt3$

Solution

Exercise 96: Solution

Let $\mathcal K$ be the kite formed by joining two right triangles with legs $2$ and $2\sqrt3$ along a common hypotenuse. Six copies of $\mathcal K$ are used to form the polygon shown below, in which the two sides of length $2\sqrt3$ of every kite meet at the point $O$. What is the area of triangle $\Delta ABC$?

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