Question

Task 4- Application

i) Draw a Quadrilateral, a Pentagon and a Hexagon

ii) Draw all the diagonals for each polygon and count the number of diagonals.

iii) Based on above, form an algebraic expression for the number of diagonals a polygon of n number of sides will

have.

iv) Find the number of diagonals in the polygons with 18 and 20 sides.

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Answer 1

Answer:

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).

Answer 2

Answer:

draw a quardileteral pentagon and a hexagon on a coloured sheet of paper mark their exterior angles taken in order at each vertex