Question

Q7 a and b is confusing, is there any chance someone could help?

Answer 1

a. 12 sides

b. Not possible

Explanation:

a.

`d=(1)/(2) n(n-3)`

`(1)/(2)n^(2)-(3)/(2) n=54`

multiply by 2

`n^(2) -3n=108`

equation

`n^(2) -3n-108=0`

factor

`(n-12)(n+9)`

`n-12=0\\n=12`

b.

`n^(2) -3n=33`

`n^(2) -3n-33=0`

The roots of the equation are decimal numbers

The number of sides must be integer

So there is no polygon with 33 diagonals.

Hope this helps