Total planar area can be estimated based on sampling by a lattice of figures (e.g. point patterns, line segments, quadrats). General formulae are provided for the approximation of mean squared errors. The approximation formulae are products of the boundary length and of a parameter that depends only on the sampling scheme. An R package is provided by the authors for the numerical computation of the mean squared error formulae. The speed of convergence of the mean squared error approximation is assessed on the basis of several simulations. Several sampling schemes are compared in view of the approximated mean squared errors.