The Triangular Field That's Smaller Than It Looks
A triangular field has two equal sides of 30 perches each and a base of 18 perches. A ninth-century method for finding its area: add the two equal sides together and take half of that (giving 30), take half of the base (giving 9), then multiply those two halves together. What area does that give — and is the method actually correct?
Reveal the answer
The method gives 30 times 9 = 270 square perches. But it's mathematically wrong: using the correct formula for a triangle's area from its three sides, the true area is only about 257.6 square perches. This is Problem 24, 'De Campo Triangulo,' from Propositiones ad Acuendos Juvenes ('Problems to Sharpen the Young'), a ninth-century collection traditionally attributed to Alcuin of York — one of twelve geometry problems in it, and a genuine record of how shaky area formulas still were in early medieval Europe.