GATE 2021 EE – Question 7
In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm$^2$ is:
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Correct answer: (C) 3.125
Explanation
The outer square has area $10\times10=100$ cm$^2$. Joining the midpoints of the sides halves the area each time, so the nested squares have areas $50,25,12.5,6.25,3.125$. The shaded square is the fifth inner square, with area $3.125$ cm$^2$.