MathNet 2023-part-07 — 187 problems (EN–VI) Question 49

In the following figure—not drawn to scale!—$E$ is the midpoint of $BC$, triangle $FEC$ has area $7$, and quadrilateral $DBEG$ has area $27$. Triangles $ADG$ and $GEF$ have the same area, $x$. Find $x$.