we have two sides and a known angle, then we use the following formula for area
[tex]=\frac{a\cdot b\cdot\sin C}{2}[/tex]where a = 8. b = 12 and C = 62°, so
[tex]\begin{gathered} A=\frac{8\cdot12\cdot\sin 62}{2} \\ A=\frac{96\cdot\sin 62}{2} \\ A=48\cdot\sin 62 \\ A=42.4 \end{gathered}[/tex]answer: 42.4 m^2
