Diamond and angles

Find the area of a diamond with a side of 5 cm if you know that the internal angles in the diamond are 60° and 120°.

Correct answer:

S =  21.6506 cm²

Step-by-step explanation:

$$\begin{gathered} a=5\text{ cm } \\ \alpha =60^{\circ } \\ \sin \alpha =h:a \\ h=a\cdot \sin {\alpha }^{\circ }=a\cdot \sin 60^{\circ }=5\cdot \sin 60^{\circ }=5\cdot 0.866025=4.33013\text{ cm } \\ S=a\cdot h=5\cdot 4.3301=21.6506{\text{cm}}^2 \end{gathered}$$

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