The perimeter of an isosceles triangle is $306\, m$ and each of the equal sides is $\frac{5}{8}$ of the base. Find the area.

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \text{ cm}$ and $26 \text{ cm}$. The area of the circle is .......... $\text{cm}^2$. [Take $\pi = \frac{22}{7}$]

If the radius of a circle is decreased by $20 \%$,then the percentage decrease in its area is (in $\%$)?

Water flows out at the rate of $10 \, m/min$ from a cylindrical pipe of diameter $5 \, mm$. Find the time taken to fill a conical tank whose diameter at the surface is $40 \, cm$ and depth is $24 \, cm$ (in $min$)?

The tangents drawn at points $A$ and $B$ of a circle with centre $O$ meet at $P$. If $\angle AOB = 120^{\circ}$ and $AP = 6 \text{ cm}$,then what is the area of triangle $APB$ (in $\text{cm}^{2}$)?

$3$ horses are tethered at $3$ corners of a triangular plot of land having sides $20 \, m$,$30 \, m$,and $40 \, m$,each with a rope of length $7 \, m$. The area (in $m^2$) of the region of this plot,which can be grazed by the horses,is (Use $\pi = \frac{22}{7}$)