Abstract Given a bounded open connected set Ω ⊂ ℝ 2 {\Omega\subset\mathbb{R}^{2}} with Lipschitz boundary, we consider the class of piecewise constant maps u taking three fixed values α , β , γ ∈ ℝ 2 {\alpha,\beta,\gamma\in\mathbb{R}^{2}} , vertices of an equilateral triangle; for any u in this class, using a weak notion of Jacobian determinant valid for BV functions, we give a precise description of Det ( ∇ u ) {\operatorname{Det}(\nabla\kern 0.569055ptu)} and show that the relaxed graph area of u is bounded from above by a quantity related to the flat norm of Det ( ∇ u ) {\operatorname{Det}(\nabla\kern 0.569055ptu)} . The provided upper bound allows to show the validity of a De Giorgi conjecture regarding the relaxed area functional when one restricts to this class of piecewise constant functions.