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imc

geometry intermediate

Problem

Each of the sides of a square with area is bisected, and a smaller square is constructed using the bisection points as vertices. The same process is carried out on to construct an even smaller square . What is the area of ?
(A)
(B)
(C)
(D)
(E)
Solution
Since the area of the large square is , the side length equals . If all sides are bisected, the resulting square has side length , thus making the area . If we repeat this process again, we notice that the area is just half that of the previous square, so the area of
Final answer
E