Answer:
i. 9
ii. 14
iii. 405
iv. [tex]\frac{n(n-3)}{2}[/tex]
Step-by-step explanation:
The number of diagonals in a polygon of n sides can be determined by:
[tex]\frac{n(n-3)}{2}[/tex]
where n is the number of its sides.
i. For a hexagon which has 6 sides,
number of diagonals = [tex]\frac{6(6-3)}{2}[/tex]
= [tex]\frac{18}{2}[/tex]
= 9
The number of diagonals in a hexagon is 9.
ii. For a heptagon which has 7 sides,
number of diagonals = [tex]\frac{7(7-3)}{2}[/tex]
= [tex]\frac{28}{2}[/tex]
= 14
The number of diagonals in a heptagon is 14.
iii. For a 30-gon;
number of diagonals = [tex]\frac{30(30-3)}{2}[/tex]
= [tex]\frac{810}{2}[/tex]
= 405
The number of diagonals in a 30-gon is 405.
iv. For a n-gon,
number of diagonals = [tex]\frac{n(n-3)}{2}[/tex]
The number of diagonals in a n-gon is [tex]\frac{n(n-3)}{2}[/tex]
