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Find the area of square

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Solvable if diagram is following

\(\therefore \) x2 + a2 = 62 = 36   .....(i)

\(sin45^\circ = \frac{x +a}{4 +6}\)

 \(x +a = \frac{10}{\sqrt2}\)      (\(\because sin45^\circ = \frac12\))

⇒ (x + a)2\(\frac{100}2 =50\) 

⇒ x2 + a2 + 2ax = 50

⇒ 2ax = 50 - 36 = 14

\(\because\) (x +a)2 = 50

⇒ x + a = 5√2   ......(i)

(x + a)2 - 4ax = 50 - 28 = 22    \((\because 2ax = 14)\)

\(\therefore \) (x - a)2 = 22

⇒ x - a = \(\sqrt{22}\)    ......(ii)

\(\therefore \) (x + a) - (x - a) = \(5\sqrt2 - \sqrt{22}\)

⇒ 2a = \(5\sqrt2 - \sqrt{22}\)

⇒ \(a = \frac{5}{\sqrt2}-\sqrt{\frac{11}2}\approx 1.19\approx 1.2\, unit\)

\(\therefore \) Area of square = a2 \(\approx\) (1.2)2 = 1.44 unit2.

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