In floor in the foyer of a school is a tiled design based on a pentagon.

How many triangles are formed?
(Hint: Some triangles are within triangles)
If you repeated the same style of design with a hexagon with every vertex connected to every other vertex, how many triangles in this shape.
Could you use this information to predict how many triangles would be in an octagon where every vertex connected to every other vertex? Explain your answer.
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