2024 AMC 10A Problem 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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.