In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AB = \sqrt{10}$ and $AM = 2.5$,then $MC = \ldots$

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

The perimeter of rhombus $ABCD$ is $68$. If $AC = 30$,find $BD$.

An aeroplane leaves an airport and flies due North at $300 \, km/h$. At the same time,another aeroplane leaves the same airport and flies due West at $400 \, km/h$. How far apart will the two aeroplanes be after $1 \frac{1}{2}$ hours (in $, km$)?

$A$ flag pole $18 \, m$ high casts a shadow $9.6 \, m$ long. Find the distance of the top of the pole from the far end of the shadow. (in $m$)

In $\Delta ABC$,$AB = AC$ and $m \angle A = 90^\circ$. If $BC = \sqrt{2} a$,then the area of $\Delta ABC$ is $\ldots \ldots \ldots \ldots$ $(a \in R^+)$.