In rhombus $ABCD$,$\overline{AC} \cap \overline{BD} = \{O\}$. Then the area of $\Delta OAB = \ldots \ldots \ldots \ldots \times$ area of $\square ABCD$.

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

In $\Delta ABC$,$\overline{AD}$ is a median and $AB^2 + AC^2 = 148$. If $AD = 7$,then $BC = \ldots$

The lengths of the diagonals of a rhombus are $16 \, cm$ and $12 \, cm$. Then,the length of the side of the rhombus is (in $cm$)

In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $\overline{AD}$ is an altitude. If $AB = \sqrt{5}$ and $BD = 2$,then the length of hypotenuse $\overline{BC}$ is.........

State whether the following statement is true or false. Justify your answer.
$\triangle ABC$ with vertices $A(-2, 0), B(2, 0)$ and $C(0, 2)$ is similar to $\triangle DEF$ with vertices $D(-4, 0), E(4, 0)$ and $F(0, 4)$.