
A regular hexagon has 3 diagonals (half the number of sides). Just like a square has 4 sides and two diagonals, because there are 2 pairs of diametrically opposite vertices. In a REGULAR hexagon, there are three pairs of diametrically opposite vertices. So there are 3 diagonals. Now if u draw a regular hexagon, and draw all the diagonals, u will observe that the hexagon has been divided into 6 triangles. These triangles are equilateral triangles with side equal side of the hexagon. So the length of one diagonal is 2a where "a" is the side of the hexagon. Therefore, the sum of the lengths of the diagonals is 6a=30. 