Rhombus 48

A large rhombus is composed of four identical smaller rhombuses, each with an area of 42 m² and an angle alpha of 60°. What is the perimeter of the large rhombus?

Final Answer:

o =  55.7121 m

Step-by-step explanation:

$$\begin{gathered} S_1=42{\text{m}}^2 \\ \alpha =60{}^{\circ } \\ {S}_1=a^2\cdot \sin \alpha \\ a=\sqrt{S_1/\sin \alpha }=\sqrt{S_1/\sin 60°}=\sqrt{42/\sin 60°}=\sqrt{42/0.866025}=6.96401\text{m} \\ b=2\cdot a=2\cdot 6.964\doteq 13.928\text{m} \\ o=4\cdot b=4\cdot 13.928=55.7121\text{m} \end{gathered}$$

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