How to calculate the area of the small red square?
The area of a square with a side of eight centimeters is equal to 8² = 64 in cm². Elementary, right? However, we do not even need this result to solve certain puzzles on the surfaces of squares!
Question:
The large square, below, measures 840 cm2. What is the measurement of the small red square in the center?
Response :
105cm²
Each element of the drawing can be built with the same basic brick: the right isosceles triangle from the top left corner.
You need two for the triangles in the middle of the sides and four for the squares. The small triangles at the corners therefore represent a square and the large triangles in the middle of the sides, two squares. In all, the large square is worth eight small squares, hence the result.
Learn more about Hervé Lehning
Normalien and agrégation in mathematics, Hervé Lehning taught his discipline for a good forty years. Crazy about cryptography, member of the Association of encryption and information security reservists, he has in particular pierced the secrets of Henri II’s cipher box.
Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.
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