What is the area of a given right-angled triangle?
$I.$ The length of the hypotenuse is $5\, cm$.
$II.$ The perimeter of the triangle is four times that of its base.
$III.$ One of the angles of the triangle is $60^{\circ}$.

In the given figure,there is a large semicircle with diameter $AB = 56 \ cm$. Inside this,there are four smaller identical semicircles with diameters $AE, EF, FG,$ and $GB$ along the diameter $AB$. $A$ circle is inscribed such that it is tangent to the large semicircle and the two middle smaller semicircles. What is the area (in $cm^2$) of the shaded region?

Two circles touch internally. The sum of their areas is $116\, \pi \, cm^2$ and the distance between their centers is $6 \, cm$. Then,the radii of the circles are?

$A$ cow is tied by a rope at the corner of a rectangular field. If the length of the rope is $14\, m$,then the area of the field which the cow could graze is.......$m^2$

$A$ 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 $\pi = \frac{22}{7}$]

$A$ General,while arranging his men,who were $6000$ in number,in the form of a square,found that there were $71$ men leftover. How many were arranged in each row?