$($a$)$ Often the mathematics of a problem in Fluid Mechanics is made

easier if we assume the mass or area to be concentrated at a single

point. What are these points known as for:

$($i$)$ mass;

$($ii$)$ area.

$($b$)($i$)$ Determine the centroid of the shape, as shown in Figure $1$

$($note that the circles are holes$)$:

Figure $1$

$($ii$)$ Determine the second moment of area of this shape and hence

its radius of gyration about the axis $a-a.$