Mock AMC 8 #1 - Problem 9

Let $ABCDEFGH$ be a regular octagon of side length $1$. Find the area of $\triangle ABE$.

$(\textbf{A})\;1\quad(\textbf{B})\;\dfrac{2+\sqrt2}{2}\quad(\textbf{C})\;\dfrac{1+\sqrt2}{2}\quad(\textbf{D})\;\dfrac{\sqrt2}{2}\quad(\textbf{E})\;\sqrt2$

Enter your answer as a capital letter.