AMC 12 2023b Problem 25

A regular pentagon with area $\sqrt{5}+1$ is printed on paper and cut out. The five vertices of the pentagon are folded into the center of the pentagon, creating a smaller pentagon. What is the area of the new pentagon?

\textbf{(A)}4-\sqrt{5} \textbf{(B)}\sqrt{5}-1 \textbf{(C)}8-3\sqrt{5} \textbf{(D)}\frac{\sqrt{5}+1}{2} \textbf{(E)}~\frac{2+\sqrt{5}}{3}