$[5$ PTS$]$ For the homogeneous, uniform cross section of an I beam, the vertical distance of the controid from the origin, $y_{hw,}$ is of interest. $[0\mathrm{.}5$ PT$]$ For this question, break the crosssoctional area into component areas, showing areas on the figure to tho right. Clearly label all components using numbers $(1,2,$ ctc$.)$ SHOW WORK.

$\{0\mathrm{.}5PT\}$ Accurately place a DO$7$ at the centroid of each component area. SHO W WORK.

PT$]$ Determine IAVi SHOW WORK above,

Answer for $A_j{y}_i$

$7$ Determine ybar, the $y$ coordinate of the centroid of the beam. SHOW WORK above, including $g$ a large CIRCLED $x$ on the figure above arces, Arov, of the shapd. Use the tablo shown below, SHOW WORK below.

$4477$A:

Answer for ATor $($including units$)$

$$ SHOW Answer for $A$ y coordinate of the cent $x$ on the figure above

Answer for $y_{\text{h}\text{a}\text{r}}$ : $42$

Determine Xhal. NO WORK REQUIRED.

Answer for $x_1$