Math CentralQuandaries & Queries


Question from nicky, a student:

Good day we're given 20 questions in geometry but there is one question that im having difficulty to answer...

The sum of sides of two polygons is 12 and the sum of their diagonals is 19. What kind of polygon are they?

Please help me... thanks...

Hi Nicky,

I would prepare a table with two columns, one for the number of sides of the polygon and the other with the number of diagonals

Sides Diagonals
3 0
4 2
5 ?

and look for two rows where the sum of the number of sides is 12 and the sum of the number of diagonals is 19.

How do you know the number of diagonals in each row? I can suggest two ways. Draw a diagram and count the number of diagonals or use an algebraic expression for the number of diagonals. Better yet, do both.


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