Diagonals connect corners of a figure. If you try to connect two corners of a three sided figure, the lines you draw will exactly mimic the sides of the figure. Because of this, a three sided figure has no diagonals.
0.5*(162-48) = 104 diagonals
0.5*(252-75) = 275 diagonals
A 4 sided quadrilateral has 2 diagonals.
1/2*(152-45) = 90 diagonals
7
9
90
54
A pentagon is a 5 sided figure.
There are 27 diagonals
There are 19