Euler characteristic and quadrilaterals of normal surfaces

Let M be a compact 3-manifold with a triangulation tau. We give an inequality relating the Euler characteristic of a surface F normally embedded in M with the number of normal quadrilaterals in F. This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial description. Secondly, we obtain an inequality relating the number of normal triangles and normal quadrilaterals of F, that depends on the maximum number of tetrahedrons that share a vertex in tau.