11. Given a regular quadrilateral pyramid $V-A B C D$ with all edges equal to $a$, the midpoints of the lateral edges $V B$ and $V D$ are $H$ and $K$, respectively. If the plane passing through points $A$, $H$, and $K$ intersects the lateral edge $V C$ at $L$, then the area of quadrilateral $A H L K$ is $\qquad$
11. $\frac{\sqrt{5}}{6} a^{2}$