problems (1) and (3) are applications of the side lengths of a 30-60-90 triangle. for (1) note that a regular hexagon can be divided into 6 equilateral triangles, each of which can be divided into 2 30-60-90 triangles.

problem (2) is an application of the side lengths of a right isosceles triangle ... note that the square is divided into two such triangles by the diagonal.