Diamond area calculation

The ABCD diamond has a circumference of 72 cm. The longer diagonal of the animal with the line segment AB angle is 30 °. Calculate the area of the ABCD diamond.

Final Answer:

S =  280.5922 cm²

Step-by-step explanation:

$$\begin{gathered} o=72\text{cm} \\ A=30{}^{\circ } \\ \alpha =2\cdot A=2\cdot 30=60{}^{\circ } \\ o=4a \\ a=o/4=72/4=18\text{cm} \\ \sin \alpha =h:a \\ h=a\cdot \sin \alpha =a\cdot \sin 60°=18\cdot \sin 60°=18\cdot 0.866025=15.58846\text{cm} \\ S=a\cdot h=18\cdot 15.5885=162\sqrt{3}=280.5922{\text{cm}}^2 \end{gathered}$$

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