Sunday Times Teaser 2946 – Pentagonal Gardens

by Nick MacKinnon

Published March 10 2019 (link)

Adam and Eve have convex pentagonal gardens consisting of a square lawn and paving. Both gardens have more than one right-angled corner. All the sides of the gardens and lawns are the same whole number length in metres, but Adam’s garden has a larger total area. Eve has worked out that the difference in the areas of the gardens multiplied by the sum of the paved areas (both in square metres) is a five-digit number with five different digits.

What is that number?