B Nirmala Shastry Solutions for Exercise 1: EXERCISE 20

If the area of the rhombus $\mathrm{ABCD}$ is $\mathrm{k}\sqrt{3} {\mathrm{cm}}^2$ in which $\mathrm{AB}=6 \mathrm{cm}$ and $\angle \mathrm{ABC}=60°$. Find the value of $k$.

In a rhombus $\mathrm{ABCD}$, $\angle \mathrm{A}=60°$ and $\mathrm{AB}=10 \mathrm{cm}$. Find the length of the diagonals.

In a given parallelogram $\mathrm{ABCD}, \mathrm{AB}=10 \mathrm{cm}, \mathrm{BC}=15 \mathrm{cm}$ and $\angle \mathrm{ABC}=30°$. Find the area of $\mathrm{ABCD}$.

In the trapezium $\mathrm{ABCD}$, $\mathrm{AB}\parallel \mathrm{DC}$ and $\angle \mathrm{C}=60°, \angle \mathrm{D}=45°$.  If $\mathrm{AB}=6 \mathrm{cm}$ and $\mathrm{BC}=4 \mathrm{cm}$, if the height of the trapezium is $k\sqrt{3} m$. Find the value of $k$.

In the trapezium $\mathrm{ABCD}$, $\mathrm{AB}\parallel \mathrm{DC}$ and $\angle \mathrm{C}=60°, \angle \mathrm{D}=45°$.  If $\mathrm{AB}=6 \mathrm{cm}$ and $\mathrm{BC}=4 \mathrm{cm}$, find the length of $\mathrm{DC}$.

In $△\mathrm{ABC}$,$\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=8 \mathrm{cm}$ and $\angle \mathrm{ABC}=150°$. Find the are of $△\mathrm{ABC}$.

In $△\mathrm{PQR}, \mathrm{PS}$ is perpendicular to $\mathrm{QR}$. If $\mathrm{PS}=6 \mathrm{cm}$, if the length of $\mathrm{QR}=k\sqrt{3}$ find the value of $k$.

In $△\mathrm{PQR}, \angle \mathrm{P}:\angle \mathrm{Q}:\angle \mathrm{R}=1:2:3$ and the altitude from $\mathrm{P}$ to $\mathrm{QR}$ is $4 \mathrm{cm}$. Find the perimeter of $△\mathrm{PQR}$.