(1) S=12bcsinA=12⋅3⋅4⋅sin60°=12⋅12⋅32=33S = \frac{1}{2}\mathrm{bc}\sin A = \frac{1}{2}\cdot 3 \cdot 4 \cdot \sin 60° = \frac{1}{2}\cdot 12 \cdot \frac{\sqrt{3}}{2} = 3\sqrt{3}S=21bcsinA=21⋅3⋅4⋅sin60°=21⋅12⋅23=33 (2) S=12acsin60°=12⋅4⋅5⋅sin60°=12⋅20⋅32=53S = \frac{1}{2}\mathrm{ac}\sin 60° = \frac{1}{2}\cdot 4 \cdot 5 \cdot \sin 60° = \frac{1}{2}\cdot 20 \cdot \frac{\sqrt{3}}{2} = 5\sqrt{3}S=21acsin60°=21⋅4⋅5⋅sin60°=21⋅20⋅23=53 (3) S=12absinC=12⋅32⋅4⋅sin45°=12⋅122⋅12=6S = \frac{1}{2}\mathrm{ab}\sin C = \frac{1}{2}\cdot 3\sqrt{2} \cdot 4 \cdot \sin 45° = \frac{1}{2}\cdot 12\sqrt{2} \cdot \frac{1}{\sqrt{2}} = 6S=21absinC=21⋅32⋅4⋅sin45°=21⋅122⋅21=6 (4) S=12absinC=12⋅2⋅2⋅sin(180−30)°=12⋅4⋅12=1S = \frac{1}{2}\mathrm{ab}\sin C = \frac{1}{2}\cdot 2 \cdot 2 \cdot \sin(180-30)° = \frac{1}{2}\cdot 4 \cdot \frac{1}{2} = 1S=21absinC=21⋅2⋅2⋅sin(180−30)°=21⋅4⋅21=1