$A$ circle is inscribed in an equilateral triangle of side $8 \text{ cm}$. The area of the portion between the triangle and the circle is ...... $\text{cm}^2$.

If the perimeter of an equilateral triangle is $12\, m$,then find its area.

$A$ rectangle has width $a$ and length $b$. If the width is decreased by $20 \%$ and the length is increased by $10 \%$,what is the area of the new rectangle as a percentage of the original area $ab$?

The area of a quadrilateral is $420 \, m^{2}$ and the perpendiculars drawn to one diagonal from the opposite vertices are $18 \, m$ and $12 \, m$. Then,the length of the diagonal is......$m$

$A$ person $A$ takes $15 \text{ seconds}$ to cross a rectangular field diagonally walking at a speed of $52 \text{ m/min}$. $A$ person $B$ takes the same time to cross the same field along its sides (length + width) walking at a speed of $68 \text{ m/min}$. The area of the field is $....... \text{ m}^2$.

$A$ $2 \text{ m}$ broad pathway is to be constructed around a rectangular plot on the inside. The area of the plot is $96 \text{ m}^2$. The rate of construction is $₹ 50 / \text{ m}^2$. Find the total cost of construction (in $₹$).