$A$ lawn is in the form of a rectangle having its breadth and length in the ratio $3:4$. The area of the lawn is $\frac{1}{12}$ hectare. The breadth of the lawn is..........$metres$.

What is the cost of flooring a rectangular hall?
Statements:
$I.$ The length of the rectangle is $6 \ m$.
$II.$ The breadth of the rectangle is $2/3$ of its length.
$III.$ The cost of flooring an area of $1 \ m^2$ is ₹ $4500$. (Note: Corrected unit/value for logical consistency).

What is the area of the following figure? (in $cm^2$)

$A$ rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

In a triangle $ABC$,$AB + BC = 12 \text{ cm}$,$BC + CA = 14 \text{ cm}$,and $CA + AB = 18 \text{ cm}$. Find the radius of the circle (in $\text{cm}$) which has the same perimeter as the triangle.

Find the area of a triangle in which each side measures $8 \text{ cm}$ (in $\sqrt{3}$)? (in $\text{sq. cm.}$)