Let's say one side's length is a. Enclosed area is a triangle with 2a as a side opposed to α (half of the side of the equal-sided triangle). Using law of sines, we can easily get other two sides because we have one angle 3π radian (as the triangle is equal-sided), so a third angle would be π−3π−α=32π−α radian.
Let's say that a side opposite to 3π angle is of length x and opposite to 32π−α is of length y.
sinα2a=sin(3π)x=sin(32π−α)y
x=2a⋅sinαsin(3π),y=2a⋅sinαsin(32π−α) .
Area is calculated as 21ab⋅sinA , where a, b are sides and A is the angle between them, so in our case it is equal to:
S=21xy⋅sinα=8a⋅sin2αsinα⋅sin(3π)⋅sin(32π−α)=
=8a⋅sinαsin(3π)⋅sin(32π−α) .
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