A rhombus has four 6-inch sides and two 120-degree angles. From one of the vertices of the obtuse angles, the two altitudes are drawn

120-degree-angles

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A rhombus has four 6-inch sides and two 120-degree angles. From one of the vertices of the obtuse angles, the two altitudes are drawn, dividing the rhombus into three pieces. Find the areas of these pieces

Answer:

So the acute angles of the rhombus is 60-degree. Now if you draw the
altitudes from the obtuse angle vertex to the opposite side, one gets a right angle triangle with hypotenuse 6-inch, and the angle opposite to the hypotenuse of the triangle is 60-degree. Similarly on the other vertex with the obtuse angle. So the three regions are a rectangle formed in the middle, and two right angle triangle with hypotenuse 6 inch and angle 60-degree.
The area of the triangles is
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