Geometry · Dissections · Equilateral pentagon · Area ratio · Comparing irrational numbers
Natasa glued a square and an equilateral triangle of the same side length into a pentagon. Out of seven copies of that pentagon she built the figure shown on the right, which sits inside a large square.
a) Prove that Natasa's figure can be inscribed in a large square exactly as the picture shows.
b) Does Natasa's figure cover more than \(\tfrac{2}{3}\) of the area of the large square?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2021, 1. letnik, category A, problem B3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source