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

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 $ABC$?

In $\triangle ABC$,$\angle A = 90^{\circ}$ and $AD \perp BC$,where $D$ lies on $BC$. If $BC = 8 \ cm$ and $AC = 6 \ cm$,then the ratio of the area of $\triangle ABC$ to the area of $\triangle ACD$ is:

$A$ tank $4 \, m$ long, $2.5 \, m$ wide, and $6 \, m$ deep is dug in a field $10 \, m$ long and $9 \, m$ wide. If the earth dugout is evenly spread over the field, the rise in level of the field will be (in $cm$):

If the radius of one circle is $12$ times the radius of another,how many times does the area of the greater circle contain the area of the smaller circle?

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 $cm^2$):