A rectangle of length ‘x’ and breadth ‘y’ is inscribed in a semi-circle of fixed radius ‘r’ as shown in the figure given below. Based on the above information answer the following question:

Area A(θ), 0 < θ < \(\frac{π}{2}\)  of the rectangle ABCD, is

r2 sin θ r2 sin2θ r2 cos2θ r2 cos θ

r2 sin2θ

$x = 2r\, cosθ$ $y = r\, sinθ$ Area(ABCD) = $2r^2cosθsinθ$ $=r^2sin2θ$ Option B is correct.