Math CentralQuandaries & Queries


Question from Nilesh, a student:

Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. How to find the area of the space enclosed by the four pieces?
Please let me know.

The answer is not unique. The centers can lie at the vertices of any rhombus with edges 14cm and two angles between 60 and 90 degrees, and this will change the area significantly. Probably you are meant to assume it's a square.

Start with the square, draw an accurate diagram, and subtract off the bits that are covered by discs.

Good Hunting!

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