Based on Ilian's comment, but modified to fit your situation.
Needs["NDSolve`FEM`"];
Ω =
MeshRegion[
{{0, 0}, {2/Sqrt[3], 0}, {1/Sqrt[3], 1}},
{Line[{{1, 2}, {2, 3}, {3, 1}}]}];
mesh = ToElementMesh[Ω, MaxCellMeasure -> 0.01, "MeshOrder" -> 1];
mesh["Coordinates"] // Length
59