Diamond ABCD

In the diamond ABCD, the diagonal e = 24 cm, and the size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.

Correct answer:

x =  54.36 cm

Step-by-step explanation:

$$\begin{gathered} e=24\text{cm} \\ \phi =28{}^{\circ } \\ w=e/2=24/2=12\text{cm} \\ \cos \phi =w:a \\ a=w/\cos \phi =w/\cos 28°=12/\cos 28°=12/0.882948=13.59084\text{cm} \\ x=4\cdot a=4\cdot 13.5908=54.36\text{cm} \end{gathered}$$

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