NRICH: Diagonals

How many diagonals does a regular icosagon (20 sides) have?

A square has 2 diagonals, a regular pentagon has 5 and a regular hexagon has 9.

How many diagonals does a regular icosagon (20 sides) have?

This problem is adapted from the South East Asian Mathematics Competition

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Age 14 to 16


Algebra & Pre-Algebra, Patterning & Sequencing
High School

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