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Let    F  (  x  ,  y  )    be a binary form of degree at least 3 and non‐zero discriminant. We estimate the area    A  F    bounded by the curve    |  F  (  x  ,  y  )  |  =  1    for four families of binary forms. The first two families that we are interested in are homogenizations of minimal polynomials of    2  cos  (    2  π   n   )    and    2  sin  (    2  π   n   )   , which we denote byΨ  n    (  x  ,  y  )andΠ  n    (  x  ,  y  )    , respectively. The remaining two families of binary forms that we consider are homogenizations of Chebyshev polynomials of the first and second kinds, denoted asT  n    (  x  ,  y  )andU  n    (  x  ,  y  )    , respectively.

ON THE AREA OF THE FUNDAMENTAL REGION OF A BINARY FORM ASSOCIATED WITH ALGEBRAIC TRIGONOMETRIC QUANTITIES