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

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......$cm^2$.

How many bricks,each measuring $25\, cm \times 15\, cm \times 8\, cm$,will be required to build a wall $10\, m \times 4\, dm \times 5\, m$ if $\frac{1}{10}$ of its volume is occupied by mortar?

The area of a rectangle is $460 \, m^2$. If the length is $15 \%$ more than the breadth,what is the breadth of the rectangular field? (in $metres$)

In $\Delta ABC$ and $\Delta PQR$,$\angle B = \angle Q$ and $\angle C = \angle R$. $M$ is the mid-point of side $QR$. If $AB : PQ = 7 : 4$,then $\frac{\text{area}(\Delta ABC)}{\text{area}(\Delta PMR)}$ is:

The largest cone is formed at the base of a cube of side measuring $7 \ cm$. Find the ratio of the volume of the cone to the volume of the cube.