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Sunday Times Teaser 2807 – Pentagons

by Nick MacKinnon

Published: 10 July 2016 (link)

I have taken five identical straight rods and joined each to the next by a hinge to make a flexible ring. With this ring I can make lots of different pentagonal shapes, and in particular I can make lots of pentagons with area equal to a whole number of square centimetres. The largest whole-numbered area achievable is a two-figure number, and the smallest whole-numbered area achievable is another two-figure number. In fact these two numbers use the same two digits but in the reverse order.

What is the largest whole-numbered area achievable?

One Comment Leave one →
  1. Brian Gladman permalink

    This gives a maximum area of 61 square centimetres with a rod length of approximately 5.954 centimetres. Interestingly, since a rod length up to about 6.05 centimetres will give the same result, the rods could be of integer length.

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