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

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $m \angle A = 60^{\circ}$. If $AC = 10$,then $AB = \dots$

If in triangles $ABC$ and $DEF$,$\frac{AB}{DE} = \frac{BC}{FD}$,then they will be similar,when

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $BM = 12$ and $AM = 9$,then $AC = \ldots$

The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

In $\Delta ABC$,$A-D-B$,$A-E-C$ and $\overline{DE} \parallel \overline{BC}$. If $AB:AC = 3:4$,which of the following holds true?