Question A.02: Locate the centroid C of the area A shown in Fig. A.10.

Selecting the coordinate axes shown in Fig. A.11, we note that the centroid C must be located on the y axis, since this axis is an axis of symmetry; thus, \bar{X}=0.

Dividing A into its component parts A_{1} and A_{2}, we use the second of Eqs. (A.6)

\overline{{{X}}}=\frac{\sum\limits_{i}\,A_{i}\overline{{{x}}}_{i}}{\sum\limits_{i}A_{i}}\ \ \ \ \overline{{{Y}}}=\frac{\sum\limits_{i}\,A_{i}\overline{{{y}}}_{i}}{\sum\limits_{i}A_{i}}     (A.6)

to determine the ordinate \bar{Y} of the centroid. The actual computation is best carried out in tabular form.

\bar{Y}=\frac{\sum_{i} A_{i} \bar{y}_{i}}{\sum_{i} A_{i}}=\frac{184 \times 10^{3} \mathrm{~mm}^{3}}{4 \times 10^{3} \mathrm{~mm}^{2}}=46 \mathrm{~mm}