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.