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Counting triangles – practice for Years 3–8

Sample questions on Counting triangles with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Logic
Year
Years 3–8
Curriculum area
Counting

Question types: How many triangles?

Rule: Counting triangles

Count step by step: small triangles, then those made of two, of three… Miss none and count none twice.

Several lines run from the top corner. Every two of them make a triangle with each horizontal line.

Example: 3 lines from the top and only the base below: 3 pairs of lines × 1 = 3 triangles.

Watch out: Don’t forget the big triangle that is the whole picture.

Sample questions

  1. Question 1 Easy

    How many triangles of all sizes are there in the picture?

    Show the solution
    Answer: 3

    How it works: 3 lines leave the top corner; any two of them with one of the 1 level lines make a triangle: 3 × 1 = 3.

  2. Question 2 Normal

    How many triangles of all sizes are there in the picture?

    Show the solution
    Answer: 10

    How it works: 5 lines leave the top corner; any two of them with one of the 1 level lines make a triangle: 10 × 1 = 10.

  3. Question 3 Hard

    How many triangles of all sizes are there in the picture?

    Show the solution
    Answer: 12

    How it works: 4 lines leave the top corner; any two of them with one of the 2 level lines make a triangle: 6 × 2 = 12.

Related topics

All Logic topics

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