[tex]a)\\d_1 = 10 \ cm\\d_2 = 6 \ cm\\\alpha = 30^{o}\\P = ?\\\\P = \frac{1}{2}d_1\cdot d_2\cdot sin\alpha\\\\P = \frac{1}{2}\cdot10\cdot6\cdot sin30^{o}=30\cdot\frac{1}{2}=\underline{15 \ cm^{2}}[/tex]
[tex]b)\\d_1 = 8\sqrt{3} \ cm\\d_2 = 4 \ cm\\\alpha = 60^{o}\\P = ?\\\\P = \frac{1}{2}d_1\cdot d_2\cdot sin\alpha\\\\P = \frac{1}{2}\cdot8\sqrt{3}\cdot4\cdot\frac{\sqrt{3}}{2}=\underline{24 \ cm^{2}}[/tex]
[tex]c)\\d_1 = 21 \ cm\\d_2 = 6\frac{2}{3} = \frac{20}{3} \ cm\\\alpha = 120^{o}\\P = ?\\\\P = \frac{1}{2}d_1\cdot d_2\cdot sin\alpha\\\\P = \frac{1}{2}\cdot21\cdot\frac{20}{3}\cdot sin120^{o} =70\cdot sin(180^{o}-60^{o}) = 70\cdot sin60^{o}=70\cdot\frac{\sqrt{3}}{2} \ cm^{2}\\\\\underline{P = 35\sqrt{3} \ cm^{2}}[/tex]
[tex]d)\\d_1 = 12 \ cm\\d_2 = 5\sqrt{2} \ cm\\\alpha = 135^{o}\\P = ?\\\\P = \frac{1}{2}d_1\cdot d_2\cdot sin\alpha\\\\P = \frac{1}{2}\cdot12\cdot5\sqrt{2}\cdot sin135^{o} = 30\sqrt{2}\cdot sin(180^{o}-45^{o}) = 30\sqrt{2}\cdot sin45^{o}=30\sqrt{2}\cdot\frac{\sqrt{2}}{2} \ cm^{2}}\\\\\underline{P = 30 \ cm^{2}}[/tex]
