1956 AHSME Problem 37

On a map whose scale is 400 miles to an inch and a half, a certain estate is represented by a rhombus having a 60^{\circ} angle. The diagonal opposite 60^{\circ} is \frac {3}{16} in. The area of the estate in square miles is:

\textbf{(A)}\ \frac{2500}{\sqrt{3}}\qquad \textbf{(B)}\ \frac{1250}{\sqrt{3}}\qquad \textbf{(C)}\ 1250\qquad \textbf{(D)}\ \frac{5625\sqrt{3}}{2}\qquad \textbf{(E)}\ 1250\sqrt{3}

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