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Question

ABCD is a square with length 15cm. Pattern of shading one quarter of the square is shown in the diagram. If this pattern is continued indefinitely, what is the area of shaded region?


  1. 75

  2. 56.25

  3. 64

  4. 90


Solution

The correct option is A

75


The largest shaded square has area 1/4 of whole square. The next one is 1/4 its size. Therefore quarter its area, so it is 116 of the whole square. Thus the total shaded area , as a fraction of whole square, is 
14+116+164+..........................
=14(114)
=1434
=13;  13×225=75

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