Sunday Times Teaser 3165 – Round the Bend
by Howard Williams
Published Sunday May 21 2023 (link)
My new craft project involves card folding and requires a certain amount of precision and dexterity. For the penultimate stage a rectangular piece of card, with sides a whole number of centimetres (each less than 50cm), is carefully folded so that one corner coincides with that diagonally opposite to it. The resulting five-sided polygon also has sides of integer lengths in cm. The perimeter of the polygon is five twenty-eighths smaller than that of the perimeter of the original rectangular card.
As a final check I need to find the new area of the card.
What, in square centimetres, is the area of the polygon?