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

**Answer Choices**

A. 4-\sqrt{5}

B. \sqrt{5}-1

C. 8-3 \sqrt{5}

D. \dfrac{1+\sqrt{5}}{2}

E. \dfrac{2+\sqrt{5}}{3}