Diagram of a right-angled triangle, with the constructed squares and the resulting hexagon.

The lengths of the two smaller sides of a right-angled triangle are \(x\) in. and \(y\) in. A square is constructed on each side of the triangle and the exterior points of the squares are joined to form a hexagon as in the diagram above. Show that the area of the hexagon is \(2(x^2 + xy + y^2)\) sq. in. Given that \(x + y = 10\), determine the minimum area of the hexagon.