Question $4(30$ marks$)$

You are tasked with analysing a composite cross$-$section used in a reinforced concrete bridge beam. This cross$-$section consists of a rectangular section with a width of $200$ mm and a height of $300$ mm $,$ a right triangular section attached to the right side of the rectangle with a base of $150$ mm and a height of $300$ mm $,$ and a circular hole located at the centre of the rectangular section with a radius of $75$ mm $,$ accommodating conduit placement. This configuration represents a segment of the bridge beam cross$-$section subjected to bending loads. As part of the design verification, determine the total moment of inertia about the $x-$ and $y-$axes for the composite section to assess its bending resistance in the beam design.

$[$C$5$: CO$2$: PO$2$: WP$1,$ WP$2,$ WP$3][30$ marks$]$