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

$A$ $5\, m$ long ladder is placed leaning against a vertical wall such that it reaches the wall at a point $4 \,m$ high. If the foot of the ladder is moved $1.6 \,m$ towards the wall,find the distance by which the top of the ladder would slide upwards on the wall (in $m$).

In $\Delta ABC$,$\overline{AM}$ and $\overline{CN}$ are altitudes. If $AB = 12$,$BC = 15$ and $AM = 9.6$,then $CN = \ldots$

In $\Delta ABC$,$m \angle A + m \angle B = m \angle C$. If $AC : BC = 3 : 4$ and $AB = 17.5$,find the perimeter of $\Delta ABC$.

In rectangle $ABCD$,$AB^{2} + BC^{2} + CD^{2} + DA^{2} = 338$,then $AC = \ldots$

In rhombus $XYZW$,$XZ = 14$ and $YW = 48$. Then,$XY = \ldots \ldots \ldots$.