Diamond PQOR

In the diamond PQOR, the diagonal RQ is 4 cm long and the angle RPQ is 60°. What is the circumference of this diamond?

Correct answer:

o =  16 cm

Step-by-step explanation:

$$\begin{gathered} RQ=4\text{ cm } \\ RPQ=60\text{ ° } \\ ROP=RPQ=60\text{ ° } \\ PRO=180-RPQ=180-60=120\text{ ° } \\ PRQ=PRO\mathrm{/}2=120\mathrm{/}2=60\text{ ° } \\ \mathrm{\Delta }RQP=60\mathrm{°}-60\mathrm{°}-60\mathrm{°} \\ RP=RQ=4\text{ cm } \\ PQ=RP=4\text{ cm } \\ o=4\cdot PQ=4\cdot 4=16\text{ cm} \end{gathered}$$

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