The side of a rhombus is $10 \mathrm{cm}$ and one of its diagonals is $12 \mathrm{cm}$. Find its perimeter and area.

If the area of the shaded portion in the following figure is $k {\mathrm{cm}}^2$, find $k$ in decimal number. [Take $\mathrm{\pi }=\frac{22}{7}$]

If the area of the shaded portion in the following figure is $k {\mathrm{cm}}^2$, find $k$ in decimal number. [Take $\mathrm{\pi }=\frac{22}{7}$]

If the area of the shaded portion in the following figure is $k {\mathrm{cm}}^2$, find $k$ in decimal number. [Take $\mathrm{\pi }=\frac{22}{7}$]

A rectangular lawn is to be surrounded externally by a path which is $3 \mathrm{m}$ wide. The dimensions of the lawn are $35 \mathrm{m}$ and $45 \mathrm{m}$. If the cost of constructing the path at the rate of $₹100$ per ${\mathrm{m}}^2$ is $₹k$, find $k$.

Two crossroads each $2 \mathrm{m}$ wide intersect each other at right angles through the centre of a rectangular area of dimension $75 \mathrm{m}\times 50 \mathrm{m}$. These crossroads run parallel to the sides of the rectangle. If the area of crossroads is $k {\mathrm{m}}^2$, find $k$.

A sheet of paper measures $40 \mathrm{cm}\times 20 \mathrm{cm}$. If a strip $4 \mathrm{cm}$ wide is cut from it all around, find the area of strip-cut out and the area of the remaining sheet of paper.

If the area of the shaded portion in the following rectangle $ABCD$ is $k$ sq. units, find $k$.