Question

Q1 To draw the diagonals of following polygons
1 quadrilateral
2 Pentagon
3 hexagon
4 heptagon
5 octagon and hence derive the general Formula for finding number of diagonals in polygon:

Answer 1

Polygon Diagonals

The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides.

For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3). However, this would mean that each diagonal would be drawn twice, (to and from each vertex), so the expression must be divided by 2.

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