Parallelogram diagonals

Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm and the angle formed by them is 30 degrees.

Correct answer:

S =  45 cm²

Step-by-step explanation:

$$\begin{gathered} u_1=15\text{ cm } \\ {u}_2=12\text{ cm } \\ {\phi }_1=30\text{ ° } \\ {\phi }_2=180-{\phi }_1=180-30=150\text{ ° } \\ x=u_1\mathrm{/}2=15\mathrm{/}2={\displaystyle \frac{15}{2}}=7.5\text{ cm } \\ y=u_2\mathrm{/}2=12\mathrm{/}2=6\text{ cm } \\ \sin {\phi }_1=h_1:y \\ {h}_1=y\cdot \sin {\phi }_1\mathrm{°}=y\cdot \sin 30\mathrm{°}=6\cdot \sin 30\mathrm{°}=6\cdot 0.5=3\text{ cm } \\ {S}_1={\displaystyle \frac{u_1\cdot h_1}{2}}={\displaystyle \frac{15\cdot 3}{2}}={\displaystyle \frac{45}{2}}=22.5{\text{cm}}^2 \\ S=2\cdot S_1=2\cdot 22.5=45{\text{cm}}^2 \end{gathered}$$

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