GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 7 of 65

Marks: +1, -0

In the figure shown below, each inside square is formed by joining the midpoints of the slides of the next larger square. The area of the smallest square (shaded) as shown, in

{cm}^{2}

is:

$1.5625$
$12.50$
$3.125$
$6.25$

Validate

Solution:

Second inner circle side,

a=√{({2.5√2}/2)^2+({2.5√2}/2)^2}

a=√{\;{5 √{2}}/{4})^{2}+(\;{5 √{2}}/{4})^{2}}

a=√{\;{2}/{16}(5 √{2})^{2}}=\;{1}/{2 √{2}}(5 √{2}) ⇒ \;{5}/{2}

Side of shaded square,

\;{a}/{2} √{2} ⇒ \;{(5 {/} 2) √{2}}/{2}=\;{5 √{2}}/{4}=\;{5}/{2 √{2}}

Area of shaded region

=(\;{a}/{2} √{2}) ⇒ \;{25}/{8}

⇒ \;{25}/{8}=3.125

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