Geometry
# Quadrilaterals

In the diagram to the right, quadrilateral $ABCD$ is a parallelogram and $M$ is the midpoint of $\overline{DC}.$

If the area of $\triangle BNC$ is $42,$ what is the area of $\triangle MNC?$

In rectangle *ABCD* (below left), $AB=3$ and $BC=5$. The corner at *C* is folded up (below right) and lands on $\overline{AB}$ so that $AC=2$ and $CB=1$.

The area of quadrilateral *CPNM* can be written as $\frac{m}{n}$, where *m* and *n* are positive, coprime integers. Find $m+n$.

What is the area of a rhombus of side 13 such that the sum of its two diagonals is 34?