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?