  Let $F(x, y)$ be a binary form of degree at least three 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
$2\cos\left(\frac{2\pi}{n}\right)$ and $2\sin\left(\frac{2\pi}{n}\right)$,
which we denote by $\Psi_n(x, y)$ and $\Pi_n(x, y)$, respectively. The
remaining two families of binary forms that we consider are homogenizations of
Chebyshev polynomials of first and second kinds, denoted $T_n(x, y)$ and
$U_n(x, y)$, respectively.
