$($b$)$ A hardwood glulam beam with a density of $\backslash (350\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ is exposed to fire on $3$ sides $($left$,$ right, bottom$).$ The timber has an original cross section of $200$ mm wide by $400$ mm deep. Using the information below:

i$.$ What are the dimensions of the timber beam after $30$ minutes in a fire?

ii$.$ What is the reduction in cross$-$section area $($expressed as a $\backslash \%)?$

iii. What is the reduction in second moment of area $($expressed as a $\backslash \%)?$

Figure $1$