The diagonals of a rhombus are $40 \, cm$ and $42 \, cm$. Find its area in $cm^2$.

Can all the angles of a quadrilateral be right angles? Give reason for your answer.

$ABCD$ is a square. If $AC = 16 \, cm$,then find the area of $ABCD$ in $cm^2$.

$AC$ is one of the diagonals of quadrilateral $ABCD$. $BM$ and $DN$ are altitudes on $AC$ from $B$ and $D$ respectively. If $AC = 18 \, cm$,$BM = 10 \, cm$,and $DN = 6 \, cm$,then $ar(ABCD) = \dots \dots \, cm^2$.

$A$ diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$. The acute angle between the diagonals is (in $^{\circ}$)

For any convex quadrilateral $ABCD$,prove that $AB + BC + CD + DA < 2(AC + BD)$.