SHAPES AND AREA/PERIMETER

Question

QUESTION ONE:
Investigate different polygons and see if you can find a relationship between the number of sides and the number of diagonals.


QUESTION TWO:
You are given the following brief by a candy manufacturing company:

We need a container for our new candy called ‘Swishers’.
It must have a volume of 1200 cm3.
Please submit 3 different ideas.

For each one, you should consider:
Amount of material needed to manufacture the container
Ease with which the containers fit together
Consumer appeal of the shape of the container

Decide which of your ideas is the best, and justify your decision

Answer 1

I offer the following explanation of # diagonals in a convex polygon having n sides.

 

There are n vertices (points). Taking two points at a time to draw distinct line segments, there are _nC₂ of them--but n of these are sides, the rest are diagonals because they don't connect 'adjacent' vertices. It helps tremendously if you draw a few polygons and test this out (visually).

Therefore # of diagonals = _nC₂ - n = ½(n)(n-1) - n = n[½(n-1) - ½(2n] = ½n(n-3)

Answer 2

ONE:

The number of diagonals of an n-sided polygon is: n(n - 3)/2

 

TWO:

You should attempt this one before asking any questions.