The interior of a quadrilateral is bounded by the graphs of (x+a y)^{2}=4 a^{2} and (a x-y)^{2}=a^{2}, where a is a positive real number. What is the area of this region in terms of a, valid for all a>0 ?

**Answer Choices**

A. \dfrac{8 a^{2}}{(a+1)^{2}}

B. \dfrac{4 a}{a+1}

C. \dfrac{8 a}{a+1}

D. \dfrac{8 a^{2}}{a^{2}+1}

E. \dfrac{8 a}{a^{2}+1}