How many four-sided figures appear in the diagram?

There are a number of these geometric combinometrics problems around.  Here is a complete graphic solution to the one of the more common ones.

Question: How many four-sided figures appear in the diagram below?

  1. 10
  2. 16
  3. 22
  4. 25
  5. 28

Answer: 25

Yaacov Apelbaum - How many four sided figures

 

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7 thoughts on “How many four-sided figures appear in the diagram?

  1. answer is 22 not 25 as question was How many “four-sided” figures appear in the diagram below? and in shape above we more than “four-sided” shapes.

    • Thanks for your comment Mahmoud, There are 25 unique 4 sided rectangle configurations in the diagram (marked in red).

      Here is the summation method I used to arrive at this figure:
      1’st row = 9
      2’nd row = 9
      3’rd row = 7
      —————
      Total = 25

  2. How do you work this out? Is it something to do with the sides I have tried counting over and over again? This is the only question i don’t understand what is the method to work it out?

    • Hi Jordan,

      You need to count all of the combinations of the four sided figures (which includes the individuals and their groupings).
      So for example, the four sided figures seen in image 1, 2, and 3 are counted individuality and the figure seen in image 13 is their unique combination.

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