The area of the incircle of an equilateral triangle of side $42 \ cm$ is (in $cm^2$)

The circumference of two circles is $132\, m$ and $176\, m$ respectively. What is the difference between the area of the larger circle and the smaller circle? (in $sq\,m$)

In a parallelogram,the lengths of adjacent sides are $12\, cm$ and $14\, cm$,respectively. If the length of one diagonal is $16\, cm$,then find the length of the other diagonal (in $cm$).

$A$ farmer wishes to start a $100 \, m^2$ rectangular vegetable garden. Since he has only $30 \, m$ of barbed wire,he fences three sides of the garden,using his house compound wall as the fourth side. The dimensions of the garden are:

The area of the largest circle that can be drawn inside a rectangle with sides $18 \, cm$ and $14 \, cm$ is (in $cm^2$):

The sides of a right-angled triangle forming the right angle are in the ratio $5: 12$. If the area of the triangle is $270 \, cm^2$,then the length of the hypotenuse is .......... $cm$.