Exercise

Construct the parallelogram $\mathrm{ABCD}$ from given measurements without using the set squares and protractor as far as possible.

$\mathrm{AB}=6.5 \mathrm{cm}, \mathrm{BC}=5.2 \mathrm{cm}$and $\angle B=45°$

Construct a trapezium $\mathrm{PQRS}$ where $\mathrm{PQ}\parallel \mathrm{RS}$ and $\mathrm{PQ}=7 \mathrm{cm}, \mathrm{QR}=3 \mathrm{cm}, \mathrm{RS}=2.5 \mathrm{cm}$ and $\mathrm{SP}=3 \mathrm{cm}$.

Construct the trapezium $\mathrm{PQRS}$ where $\mathrm{PQ}\parallel \mathrm{RS}$ and $\mathrm{PQ}=3.7 \mathrm{cm}, \mathrm{RQ}=3 \mathrm{cm}, \angle \mathrm{P}=129°$ and $\angle \mathrm{Q}=45°$.

Construct a trapezium $\mathrm{PQRS}$ where $\mathrm{PQ}\parallel \mathrm{RS}$ and $\mathrm{PQ}=7.5 \mathrm{cm}, \mathrm{QR}=4 \mathrm{cm}, \mathrm{RS}=3 \mathrm{cm}$ and $\mathrm{SP}=3.5 \mathrm{cm}$. Also, measure $\angle \mathrm{QPS}$.

Construct a trapezium $\mathrm{ABCD}$ in which $\mathrm{AB}\parallel \mathrm{DC}$, $\mathrm{AB}=4 \mathrm{cm}$, $\angle \mathrm{ABC}=120°$, $\mathrm{BC}=2.5 \mathrm{cm}$, $\mathrm{DA}=2.4 \mathrm{cm}$ and $\angle \mathrm{DAB}$ is obtuse. Also, find the measure of $\mathrm{AC}$.

Construct a trapezium $\mathrm{ABCD}$ in which $\mathrm{AB}\parallel \mathrm{DC}$, $\mathrm{AB}=6.5 \mathrm{cm}$, $\mathrm{CD}=3 \mathrm{cm}$, $\mathrm{AC}=7 \mathrm{cm}$ and $\mathrm{DB}=8.5 \mathrm{cm}$.

Regular hexagon on a side of $4 \mathrm{cm}$. Find out its area after construction.

Regular hexagon on a side of $3.2 \mathrm{cm}$. Find out its area after construction.