2005 AMC 10A Problem 20

An equiangular octagon has four sides of length 1 and four sides of length \sqrt{2}/2, arranged so that no two consecutive sides have the same length. What is the area of the octagon?

\textbf{(A) } \frac{7}{2}\qquad \textbf{(B) } \frac{7\sqrt{2}}{2}\qquad \textbf{(C) } \frac{5+4\sqrt{2}}{2}\qquad \textbf{(D) } \frac{4+5\sqrt{2}}{2}\qquad \textbf{(E) } 7

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