Find the number of diagonals of
(i) a hexagon, (ii) a decagon, (iii) a polygon of 18 sides.

Answer

(i) 9 (ii) 35 (iii) 135

Explanation

(i) Number of diagonals of a hexagon `=(.^(6)C_(2)-6)=(15-6)=9`.
(ii) Number of diagonals of a decagon `=(.^(10)C_(2)-10)=(45-10)=35`.
(iii) Number of diagonals of a polygon of 18 sides `=(.^(18)C_(2)-18)=135`.