A trapezium is formed by the pair of tangents of parabola P: y = x^...

The equation of the tangents from the centre of the ellipse to the parabola are $y = \pm x$

The equation of the tangent at the vertex $P$ of the parabola& is $y = 1$

The equation of the tangent at the end point of the minor axis of the ellipse is $y = \dfrac{1}{2}$

Hence, the area of trapezium $ABCD= \dfrac{1}{2} ⋅ \dfrac{1}{2} \left(1 + 2\right) = \dfrac{3}{4}$& sq. units