Triangle in Triangle

The side lengths of the small triangle are half of the side lengths of the big triangle. So the side lengths are $12.5,13$ and $14$ . Using the Herons Formula, the semiperimeter, $s$ is $\dfrac{12.5+13+14}{2}=19.75$ . So the desired area is $\sqrt{19.75(19.75-12.5)(19.75-13)(19.75-14)} \approx \boxed{74.55~cm^2}$

Semiperimeter $s=\frac{79}{2}$

Area of large triangle $=\sqrt{s(s-25)(s-26)(s-28)}=298.19$

Area of small triangle is quarter of that, sides being half as long, $=74.55$