Area of a Pentagon!

Geometry Level 4

Let \(S\) be the area of the convex pentagon \(ABCDE\) having the following specifications:

  • \(AB = BC\); \(CD = DE\)

  • \(BD = 2\)

  • \(\angle ABC = 150^\circ\); \(\angle CDE = 30^\circ\)

Find the value of \(S^2\).

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