Process$-$Oriented Problem $05\mathrm{.}002-$ First Moments of an Area

The cross section of a $30in.12in.$ rectangular shaped duct is shown below. The centroid of the duct is located at

point $C$ in the system. The horizontal axis, $c^{\text{'}},$ passes through the centroid of the area of the duct and divides it into two

component areas. Each area is labeled with a different color for resolution. The $x-$axis runs along the bottom edge of

the duct. The $y-$axis runs right through the middle of the duct, dividing it exactly in half, and passes through the centroid.

The mass of the duct is uniformly distributed throughout the entire duct. It is ultimately desired to determine the first

moments of the areas of each component area of the duct with respect to the horizontal axis $c^{\text{'}}.$ Before this can be

accomplished, though, the centroids of the two component areas of the duct must be found.

Process$-$Oriented Problem $05\mathrm{.}002.$d $-$ First Moments of an Area

Now that the centroid coordinates for the rectangular duct have been found, what is the area of the component section of the duct

that lies above the horizontal axis $c^{\text{'}},$ which passes through the centroid of the duct? Choose the correct answer from the following

options.

Multiple Choice

$110\mathrm{.}7$ in ${?}^2$

$114\mathrm{.}3$ in ${?}^2$

$108$ in ${?}^2$

$117$ in ${?}^2$

$105\mathrm{.}3$ in ${?}^2$