Explanation:
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 = \(\frac{12}{h} \sqrt{6}\)