In this question, you need to apply Heron's formula
[tex]\begin{gathered} A=\sqrt[]{(S\cdot(S-PQ)\cdot(S-QR)\cdot(S-PR))} \\ \end{gathered}[/tex]
Where S is the semi perimeter
[tex]\begin{gathered} S=\frac{PQ+QR+PR}{2} \\ \end{gathered}[/tex]
Therefore
[tex]\begin{gathered} S=\frac{PQ+QR+PR}{2} \\ S=\frac{7.3+9.6+14.7}{2} \\ S=\frac{31.6}{2} \\ S=15.8 \end{gathered}[/tex][tex]\begin{gathered} A=\sqrt[]{(S\cdot(S-PQ)\cdot(S-QR)\cdot(S-PR))} \\ A=\sqrt[]{(15.8\cdot(15.8-7.3)\cdot(15.8-9.6)\cdot(15.8-14.7))} \\ A=\sqrt[]{(15.8\cdot8.5\cdot6.2\cdot1.1)} \\ A=\sqrt{915.926} \\ A=30.264\text{ }cm^{2} \end{gathered}[/tex]
Now, let's calculate the requested height from
[tex]\begin{gathered} \text{Area}=\frac{b\cdot h}{2} \\ \text{30.264}=\frac{9.6\cdot h}{2} \\ h=\frac{30.264\cdot\:2}{9.6} \\ h=\frac{60.528}{9.6} \\ h=6.305\text{ cm} \end{gathered}[/tex]
