NRICH: Picturing Triangular Numbers

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Imagine two copies of a triangular array of squares. Can you picture how to fit them together to make a rectangle? What is special about the dimensions of your rectangle?

Use the interactive to test your ideas.

What do you notice about doubling triangular numbers?
Experiment with different triangle numbers and explain what is special about the rectangles made from two identical triangle numbers.

Can you write down the dimensions of the rectangle made from two copies of the 250th triangle number? Can you use this to work out the 250th triangle number?

Check – your answer should be somewhere in this list:
29184, 31375, 586594, 908475, 2092035

Deduce a strategy for working out any triangle number.

Age 11 to 14


Algebra & Pre-Algebra, Patterning & Sequencing
Middle School, High School, Educator

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NRICH (University of Cambridge)

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Online Interactive Activity

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