The area is [tex]9\sqrt{3}un^2.[/tex]
Note that: triangle AOB is an equilateral triangle because:
OA = OB (both are radius)
So ∠OAB = ∠OBA
Given that ∠AOB=60 degree.
The sum of three angles of a triangle is 180 degrees.
So,
∠OAB + ∠OBA + ∠AOB = 180
∠OAB + ∠OBA + 60 = 180
∠OAB + ∠OBA = 120
∠OAB + ∠OAB = 120
2∠OAB = 120
∠OAB = 60
It means ∠OAB = ∠OBA =60.
Since all the angles of these triangle is 60 degree, so triangle AOB is an equilateral triangle.
Given: side length = a = 6.
The area of the triangle is: [tex]\frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{3}}{4}\left(6^{2}\right)=\frac{\sqrt{3}}{4}\left(36\right)=9\sqrt{3}[/tex]
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