Find the length of a diagonal $\left(QT\right)$ of a regular pentagon that has sides of length $10 \mathrm{cm}$. Give your answer to the nearest whole number.
     

The diagram shows a regular pentagon with side $2 \mathrm{cm}$. $O$ is the centre of the pentagon.
Find angle $AOE$.

The diagram shows a regular pentagon with side $2 \mathrm{cm}$. $O$ is the centre of the pentagon.
Find angle $AOM$.

   

The diagram shows a regular pentagon with side $2 \mathrm{cm}$. $O$ is the centre of the pentagon.

Use trigonometry on triangle $AOM$ to find the length $OM$.

The diagram shows a regular pentagon with side $2 \mathrm{cm}$. $O$ is the centre of pentagon.

Find the area of triangle $AOM$