Total marks: $120.$ Each question carries $20$ marks. You must answer six questions.

Question $1$

Calculate the following for the cross$-$section shown in Figure Q$\mathrm{.}1.$

a$)$ Determine the position of the centroid from the horizontal axis $x-x.$

b$)$ Calculate the second moment of area about the horizontal axis $x-x.$

$(5)$

c$)$ Calculate the second moment of area about the centroid for the cross$-$section.

$(5)$

$(5)$

d$)$ Discuss the importance of the centroid and the second moment of area values in engineering design.

$(5)$

Figure Q$.1.$