Let P(X,Y,Z) denote a homogeneous polynomial in ℂ[X,Y,Z] such that X_P = {(u : v : w) ∈ ℂℙ² | P(u,v,w) = 0} defines a smooth complex projective curve in ℂℙ². It inherits a Riemannian metric from the Fubini-Study metric on ℂℙ².

Is there an explicit formula or algorithm that gives the area of X_P as a real surface in terms of the polynomial P(X,Y,Z)?