A square with side ' a ' is revolved about its centre through 45^{\circ}. What is the area common to both the squares?

Correct Answer is : 2(2−1)a2 sq units

{(\sqrt{2}+1) a^{2}}/{2} sq units

NIMCET 2009 Question Paper with solutions

Question : 19 of 120

Marks: +1, -0

A square with side ' a ' is revolved about its centre through

45^{∘}

. What is the area common to both the squares?

Solution:

\Side=a ⇒

Diagonal

=√{2 a}

E B^{'}=(\;{√{2}-1}/{2}) a

→ E F=E B^{'}

F C=\;{a}/{2}-(\;{√{2}-1}/{2}) a=(\;{2-√{2}}/{2})

Thus, area common to the two squares

=a^{2}-4 × \;{1}/2[({2-√2}/{2})a]^2

=a^{2}[1-\;{6-4 √{2}}/{2}]

=a^{2}[1-(3-2 √{2})]

=(2 √{2}-2 a^{2}

=2(√{2}-1) a^{2} {sq}

units

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