Math CentralQuandaries & Queries


Question from s, a student:

how to construct a triangle whose area is equal to the area of a given square?


If you start with a rectangle and cut it along a diagonal you get a triangle with half the area of the rectangle.

rectangle and triangle

Thus you can start with a square, expand it to a rectangle with twice the area and then cut it along a diagonal to obtain a triangle with the same area as the original square.

I hope this helps,

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