The perimeter of a non-square rhombus is $20 \, cm$. One of its diagonals is $8 \, cm$. The area of the rhombus is.........$cm^2$

The ratio of bases of two triangles is $x: y$ and that of their areas is $a: b$. Then the ratio of their corresponding altitudes will be

The diameter of a circle circumscribing a square is $10 \, cm$. Its sides will be

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?

If half the diagonal of a square is $5 \, cm$,then the area of the square is

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.