In the given figure,circle $P$ has a diameter of $2 \ m$ and circle $Q$ has a diameter of $1 \ m$. Find the area of the shaded region.

$A$ square has an area of $200\, m^2$. $A$ new square is formed such that the length of its diagonal is $\sqrt{2}$ times the diagonal of the given square. What is the area of the new square in $m^2$?

If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter,then $X$ is

Find the perimeter (in $cm$) of a semicircle of radius $28\, cm$.

$A$ $2 \text{ m}$ 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 $₹$).

If the ratio of areas of two squares is $225: 256,$ then the ratio of their perimeters is