$ABC$ is a triangle and $G$ is its centroid. If $AD=12 \mathrm{cm}, BC=8 \mathrm{cm}$ and $BE=9 \mathrm{cm}$, find the perimeter of $∆BDG$.

In $∆ABC,S$ is the circumcentre, $BC=72 \mathrm{cm}$ and $DS=15 \mathrm{cm}$. Find the radius of its circumcircle.

Identify the incentre of the triangle $PQR$.

Construct a quadrilateral DEAR with $DE=6 \mathrm{cm},EA=5 \mathrm{cm},AR=5.5 \mathrm{cm},RD=5.2 \mathrm{cm}$ and $DA=10 \mathrm{cm}$. Also find its area.

Construct a quadrilateral NICE with $NI=4.5 \mathrm{cm}, IC=4.3 \mathrm{cm}, NE=3.5 \mathrm{cm}, NC=5.5 \mathrm{cm}$ and $IE=5 \mathrm{cm}$. Also find its area.

Construct a quadrilateral MATH with $MA=4 \mathrm{cm},AT=3.6 \mathrm{cm},TH=4.5 \mathrm{cm}$, $MH=5 \mathrm{cm}$ and $\angle A=85°$. Also find its area.

Construct a quadrilateral $ABCD$ with $AB=7 \mathrm{cm},AD=5 \mathrm{cm},CD=5 \mathrm{cm},\angle BAC=50°$ and $\angle ABC=60°$. Also find its area.

Construct a quadrilateral $PQRS$ with $PQ=QR=5 \mathrm{cm},\angle QPR=50°,\angle PRS=40°$ and $\angle RPS=80°$. Also find its area.

Construct a trapezium BOAT in which $\overline{BO}$ is parallel to $\overline{TA},BO=7 \mathrm{cm},OA=6 \mathrm{cm}$$\mathit{,}BA=10 \mathrm{cm}$ and $TA=6 \mathrm{cm}$. Also find its area.