In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 6$,$MB = 12$ and $AN = 8$,find $AC$.

In quadrilateral $ABCD$,$P$ is the midpoint of $\overline{BC}$. If $\overline{DP}$ produced intersects $\overline{AB}$ produced at $Q$,prove that $AB = 2CD$ given that $ABCD$ is a parallelogram.

The length of a diagonal of a square is $10$. Then,its area is......

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$SY = 4.5$ and $XT = 8$,find $XZ$.

In a rhombus,the diagonals measure $10$ and $24$. Then,the length of each side of the rhombus is...........

The perimeter of an equilateral triangle is $18$. Then,the length of its altitude is $\ldots \ldots \ldots$