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

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

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

## Otвет

27.00