Lintels such as that shown in Figure $7$a span openings such as doors and windows, and support the load positioned above the aperture. They come in various forms depending on the application.

A box lintel has been specified for a particular building project. The cross$-$section of the lintel is shown in Figure $7b.$

$($a$)$

$($b$)$

The second moment of area can be calculated by considering the cross$-$section as a combination of a hollow box section and a horizontal flange. By separating the cross$-$section in this way and by using the principle of the parallel axes, answer the questions below to determine the second moment of area about the horizontal axis through the centre of area.

Whow that the second moment of area about the centre of area for the box and horizontal flange sections are $9\mathrm{.}28{10}^{6}m{m}^4$ and $2\mathrm{.}07{10}^{6}m{m}^4$ respectively $($to three sig. fig.$).$

ii$.$ Therefore, show that the second moment of area of the complete section, as shown in Figure $7b,$ about its centre of area is approximately $11\mathrm{.}4{10}^{6}m{m}^4($to three sig. fig.$).$