How many distinct diagonals of a convex hexagon can be drawn?

Question

How many distinct diagonals of a convex hexagon can be drawn?

Answer 1

hexagon ABCDEF

from point A, you can draw 3, 1 each to C, D, and E

from point B, you can draw 3, 1 each to D, E, and F

from point C, you can draw 2, 1 each to E and F

from point D, you can draw 1 to F

total number of diagonals is 3+3+2+1=9

you can use the formula n(n-3)/2=6(6-3)/2=6*3/2=18/2=9

there are n starting points but the diagonal can't end where it began and can't end at either neighboring points,

therefore a diagonal goes to (n-3) ending points

there are n points so multiply n-3 by n to begin with

n(n-3) so far

because each diagonal's ending point can be used as a starting point, the product n(n-3) counts each diagonal twice; that's why you divide by 2

n(n-3)/2 is the formula to use where n=# of sides

Answer 2

A convex polygon is one where all interior angle measurements are less than 180 degrees, and the hexagon means 6 sides.  To get diagonals, you draw a line to connect an angle to another angle (never to sides), and count up how many different lines you get.  In this case, you can draw 9.

You can also use this formula (n(n-3))/2 where n= number of sides in a polygon.