The perimeter of an equilateral triangle is $12$. Then,its area is............

If $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow ZYX$,and given $PQ = 6$,$QR = 8$,and $XY = 12$,find the length of $YZ$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x+1$,$MB = x$,$AN = 3x-3$ and $NC = 4x-10$,then $x = \dots$

In $\Delta ABC$,$A-D-B$,$A-E-C$ and $\overline{DE} \parallel \overline{BC}$. If $AD = 8$,$AB = 12$ and $AE = 12$,find $EC$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$,$AC = 15$ and $AD = 8.5$,find $BC$.

$\Delta DEF$ and $\Delta PQR$ are similar triangles if $m \angle D = m \angle R$ and $\ldots \ldots$