2. Given the ellipse $\frac{x^{2}}{2}+y^{2}=1$ with two foci $F_{1}$ and $F_{2}$, a chord $A B$ is drawn through the right focus $F_{2}$ with an inclination angle of $45^{\circ}$. Then the area of $\triangle A B F_{1}$ is $\qquad$.