[ Coordinate method on the plane [ The ratio of the areas of triangles with a common base or common height]

 ] On the coordinate plane, points $A(1 ; 3), B(1 ; 9), C(6 ; 8)$, and $E(5 ; 1)$ are given. Find the area of the pentagon $A B C D E$, where $D$ is the point of intersection of the lines $A C$ and $B E$.
If $y_{1} \neq y_{2}$ and $x_{1} \neq x_{2}$, then the equation of the line passing through the points ( $x_{1} ; y_{1}$ ) and $\left(x_{2} ; y_{2}\right)$ is

$$
\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}
$$

## Answer

21.00