A\(\bigtriangleup\) = \(\sqrt{S(S - a) (S - b)(S - c)}\) (Hero's Formula)

S = \(\frac{a + b + c}{2}\) = \(\frac{5 + 6 + 7}{2}\)

\(\frac{18}{2} = 9\)

A\(\bigtriangleup\) =  \(\sqrt{9 \times 4 \times 3 \times 2}\)

\(\sqrt{216} = 6 \sqrt{6}cm^3\)

A\(\bigtriangleup\) = \(\frac{1}{2} \times 6 \times h\)

6\(\sqrt{6} = \frac{1}{2} \times 7 \times h\)

h = \(\frac{12}{7} \sqrt{6}\)cm