$A$ lawn is in the form of a triangle having its base and height in the ratio $2:3$. The area of the lawn is $\frac{1}{12}$ hectare. Find the base and height of the lawn.

An open box is made of wood $2\, cm$ thick. Its internal length is $86\, cm,$ breadth $46\, cm$ and height is $38\, cm.$ The cost of painting the outer surface of the box at $Rs.$ $10$ per $m^2$ is? (in $Rs.$)

$A$ can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter,then the time required by $A$ to go round the new path once,travelling at the same speed as before,is (in $min$)

The length of a rectangle is $2 \, cm$ more than its breadth. The perimeter is $48 \, cm$. The area of the rectangle (in $cm^2$) is?

If a wire is bent into the shape of a square,then the area of the square is $81 \, cm^2$. When the wire is bent into a semi-circular shape,the area of the semi-circle will be (in $cm^2$):

If the diagonals of a rhombus are $8$ and $6,$ then the square of its side is