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rishabhmishra

If each of the line segments in the figure above has a length equal to 4, and the angle a,b and c are each 60 degrees, what is the total area of the shaded figure?

A. 16
B. \(8\sqrt{3}\)
C. \(24\sqrt{2}\)
D. 36
E. \(24\sqrt{3}\)

Source :- globalexperts

Attachment:
Screenshot (72).png

Since, all the sides are equal & each of the parallelograms has 60-120-60-120 angle measures, we can deduct that all of the 3 parallelograms must be Rhombuses.
Area of a Rhombus = (side)^2 * sin(any inscribed angle°)
so, Area of 1 Rhombus = 4^2* sin60° = 16*(√3/2)=8√3
Total Shaded Area = Area of 3 Rhombus = 3*8√3 = 24√3
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