for A, B, C, A1, B1, C1 being Point of (TOP-REAL 2)
for lambda, mu, nu being Real st A1 = ((1 - lambda) * B) + (lambda * C) & B1 = ((1 - mu) * C) + (mu * A) & C1 = ((1 - nu) * A) + (nu * B) holds
the_area_of_polygon3 (A1,B1,C1) = ((((1 - lambda) * (1 - mu)) * (1 - nu)) + ((lambda * mu) * nu)) * (the_area_of_polygon3 (A,B,C))