We divide the area into 2 rectangles and assume the mass of each rectangle is concentrated at the center.

Centroid of an irregular shape

Left rectangle: `"Area" = 3 × 2 = 6\ "sq unit"`. Center `(-1/2, 1)`

Right rectangle: `"Area" = 2 × 4 = 8\ "sq unit"`. Center `(2, 2)`

Taking moments with respect to the y-axis, we have:

`6(- 1/2)+8(2)=(6+8)barx`

`-3+16=14 barx`

`barx = 13/14`

Now, w.r.t the x-axis:

`6(1)+8(2)=(6+8)bary`

`6+16=14bary`

`bary=22/14`

`=1 4/7`

So the centroid is at: `(13/14, 1 4/7)`

We would use this process to solve the tilt slab construction problem mentioned at the beginning of this section.