Problem 13. In triangle $A B C$, the lengths of its medians are known: $m_{a} ; m_{b} ; m_{c}$. Find the area of this triangle.
Solution. As is known, medians of any triangle can form a triangle. The area of such a triangle is $\frac{3}{4}$ of the area of triangle $A B C$, i.e., $S_{m}=\frac{3}{4} S_{A B C}$. Then the solution to the problem is quite obvious:

using Heron's formula, we find $S_{m}$ (its sides: $m_{a} ; m_{b} ; m_{c}$); after which we find the area of triangle $A B C: S_{A B C}=\frac{4}{3} S_{m}$.