Parallelogram

The sides of the parallelogram are 8 cm and 6 cm long and the angle of the diagonals is 60°. What is its area?

Correct answer:

S =  66.954 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{ cm } \\ b=6\text{ cm } \\ X=60\text{ ° } \\ Y=180-X=180-60=120\text{ ° } \\ {S}_1=\mathrm{\Delta }BCS=b-b-b \\ {S}_2=\mathrm{\Delta }BSA=a-b-b \\ {S}_1=\sqrt{3}\mathrm{/}4\cdot b^2=\sqrt{3}\mathrm{/}4\cdot 6^2=9\sqrt{3}{\text{cm}}^2\doteq 15.5885{\text{cm}}^2 \\ s={\displaystyle \frac{a+b+b}{2}}={\displaystyle \frac{8+6+6}{2}}=10\text{ cm } \\ {S}_2=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-b)}=\sqrt{10\cdot (10-8)\cdot (10-6)\cdot (10-6)}=8\sqrt{5}{\text{cm}}^2\doteq 17.8885{\text{cm}}^2 \\ S=2\cdot S_1+2\cdot S_2=2\cdot 15.5885+2\cdot 17.8885=66.954{\text{cm}}^2 \end{gathered}$$

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