Question A.2: Locate the centroid C of the area A shown in Fig. A.9a...

Selecting the coordinate axes shown in Fig. A.9b, note that the centroid C must be located on the y axis, since this is an axis of symmetry. Thus, \bar{X} = 0.

Divide A into its component parts A_1 \text { and } A_2 and use the second of Eqs. (A.6) \bar{X}=\frac{\sum_i A_i \bar{x}_i}{\sum_i A_i} \quad \bar{Y}=\frac{\sum_i A_i \bar{y}_i}{\sum_i A_i} 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 \ mm ^3}{4 \times 10^3 \ mm ^2}=46 \ mm