Answer:
[tex]684\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The area of any triangle is equal to [tex]A=\frac{1}{2}\cdot a\cdot b\cdot \sin C[/tex], where [tex]a[/tex] and [tex]b[/tex] are two sides of a triangle and [tex]C[/tex] is the angle between them.
Plugging in given values, we have:
[tex]A=\frac{1}{2}\cdot 27\cdot 82\cdot \sin 162^{\circ}=\boxed{684\:\mathrm{cm^2}}[/tex]
