1. ## Equal Areas of triangles and quadrilateral

Hello,

Given an arbitrary convex quadrilateral ABCD.
K is the center point of line segment AB.
M is the center point of line segment CD.
$AM \cap KD=N$, $BM \cap KC=L$.
Prove that: $Area(KLMN)=Area(\triangle AND) + Area (\triangle BCL)$.

In attachment is picture.

Thank you!

2. Hint: Using the fact that the altitude from K to DC is the arithmetic mean of the altitudes from A and B, prove that the $\mathop{\mathrm{Area}}(\triangle ADM)+\mathop{\mathrm{Area}}(\triangle BMC)=\mathop{\mathrm{Area}}(\triangle KDC)$.