Answer:
i. 9
ii. 14
iii. 405
iv.
Step-by-step explanation:
The number of diagonals in a polygon of n sides can be determined by:
where n is the number of its sides.
i. For a hexagon which has 6 sides,
number of diagonals =
=
= 9
The number of diagonals in a hexagon is 9.
ii. For a heptagon which has 7 sides,
number of diagonals =
=
= 14
The number of diagonals in a heptagon is 14.
iii. For a 30-gon;
number of diagonals =
=
= 405
The number of diagonals in a 30-gon is 405.
iv. For a n-gon,
number of diagonals =
The number of diagonals in a n-gon is