The perimeter of a triangle is $16 \text{ cm}$, one of the sides is of length $6 \text{ cm}$. If the area of the triangle is $12 \text{ cm}^2$, then the triangle is:

In a $\triangle ABC$,$D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE \parallel BC$. Suppose $BE$ and $CD$ intersect at $O$. If the areas of $\triangle ADE$ and $\triangle ODE$ are $3$ and $1$ respectively,find the area of $\triangle ABC$.

In a triangle $ABC$,$AD$ and $BE$ are medians. If $AD=4$,$\angle DAB = \frac{\pi}{6}$ and $\angle ABE = \frac{\pi}{3}$,then the area of $\triangle ABC$ is

If the points $(2k, k), (k, 2k)$ and $(k, k)$ with $k > 0$ enclose a triangle of area $18$ square units,then the centroid of the triangle is equal to

In a $\triangle ABC$ with $\angle A < \angle B < \angle C$,points $D, E, F$ are on the interior of segments $BC, CA, AB$ respectively. Which of the following triangles cannot be similar to $\triangle ABC$?

The equations of the sides $AB$,$BC$,and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 21a$ $(a \neq 0)$,and $x - y = 3$ respectively. Let $P(2, a)$ be the centroid of $\triangle ABC$. Then $(BC)^2$ is equal to $........$