Geometry
# Area of Triangles

Which of the following triangles has a larger area:

- triangle A with side lengths $13, 13, 10$, or
- triangle B with side lengths $13, 13, 24\, ?$

In a square $ABCD$, $E$ and $F$ are the midpoints of sides $AB$ and $AD$, respectively. A point $G$ is taken on segment $CF$ in such a way that $2CG=3FG$.

If the side of the square is $2$, then what is the area of $\triangle{BEG}$?

Find the area of a triangle with sides $\sqrt{13}, \sqrt{61} , \sqrt{80}$.