Karen Morrison and Nick Hamshaw Solutions for Exercise 8: Exercise 15.8

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 $AOM$

Find the area of regular octagon with side $4 \mathrm{cm}$.

Find the area of regular pentagon with side $2a \mathrm{m}$.

If the area of a regular pentagon with side $2a$ meters is $k{a}^2 {\mathrm{m}}^2$, then find the value of $k$. (Express your answer correct up to three decimal places)
 

Find the area of a regular polygon with $n$ sides, each of length $2a$ metres.