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    OlympiadMediumGeometry5–6

    The Turning Square

    O Quadrado que Roda

    A square of side 44 cm is placed so that one of its corners sits exactly at the centre of a second square of side 44 cm, and it is then turned about that centre into any position. What is the area of the overlapping region, in cm²?

    The fixed square is carried to itself by a quarter turn about its centre; ask what that symmetry does to the piece that is gained and the piece that is lost.

    Solution

    Step 1 of 4

    1. 1.Draw the two lines through the centre of the fixed square parallel to its sides. They cut it into four congruent quarters, each of area 164=4\frac{16}{4} = 4 cm².