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.

In the given figure,$ABCD$ is a square of side $14 \ cm$. $E$ and $F$ are mid-points of sides $AB$ and $DC$ respectively. $EPF$ is a semicircle whose diameter is $EF$. $LMNO$ is a square. What is the area (in $cm^2$) of the shaded region?

In $\Delta ABC,$ a line through $A$ cuts the side $BC$ at $D$ such that $BD : DC = 4 : 5.$ If the area of $\Delta ABD = 60 \, cm^2,$ then the area of $\Delta ADC$ is......$cm^2$.

Find the area of a rhombus one of whose diagonals measures $10 \text{ cm}$ and the other $12 \text{ cm}$. (in $\text{cm}^2$)

The sides of a triangle are $50 \, cm$,$78 \, cm$,and $112 \, cm$. The smallest altitude is $........... \, cm$.

The circumference of a circle is $176\, m$. Then,its area is