7.61 Let $a, b, c$ and $d$ be the lengths of the sides $MN, NP, PQ$ and $QM$ of quadrilateral $MNPQ$, respectively. If $A$ is the area of $MNPQ$, then
(A) $A=\left(\frac{a+c}{2}\right)\left(\frac{b+d}{2}\right)$ if and only if $MNPQ$ is a convex quadrilateral.
(B) $A=\left(\frac{a+c}{2}\right)\left(\frac{b+d}{2}\right)$ if and only if $MNPQ$ is a rectangle.
(C) $A \leqslant\left(\frac{a+c}{2}\right)\left(\frac{b+d}{2}\right)$ if and only if $MNPQ$ is a rectangle.
(D) $A \leqslant\left(\frac{a+c}{2}\right)\left(\frac{b+d}{2}\right)$ if and only if $MNPQ$ is a parallelogram.
(E) $A \geqslant\left(\frac{a+c}{2}\right)\left(\frac{b+d}{2}\right)$ if and only if $MNPQ$ is a parallelogram.
(28th American High School Mathematics Examination, 1977)