Answer
$$A \approx 78{{\text{m}}^{\text{2}}}$$
Work Step by Step
$$\eqalign{
& a = 12{\text{m}},\,\,\,b = 16{\text{m,}}\,\,\,c = 25{\text{m}} \cr
& \cr
& {\text{First}},{\text{ find the semiperimeter }}s \cr
& s = \frac{1}{2}\left( {a + b + c} \right) \cr
& s = \frac{1}{2}\left( {12 + 16 + 25} \right) \cr
& s = \frac{{53}}{2} \cr
& \cr
& {\text{Now use Heron's formula to find the area }}A \cr
& A = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \cr
& A = \sqrt {\frac{{53}}{2}\left( {\frac{{53}}{2} - 12} \right)\left( {\frac{{53}}{2} - 16} \right)\left( {\frac{{53}}{2} - 25} \right)} \cr
& A = \sqrt {\frac{{53}}{2}\left( {\frac{{29}}{2}} \right)\left( {\frac{{21}}{2}} \right)\left( {\frac{3}{2}} \right)} \cr
& {\text{Use a calculator}} \cr
& A \approx 78{{\text{m}}^{\text{2}}} \cr} $$
