The centroid of a composite area is the weighted average of the centroids of its parts: $\bar{x}=\frac{\sum A_i{\bar{x}}_i}{\sum A_i}$ and $\bar{y}=\frac{\sum A_i{\bar{y}}_i}{\sum A_i}$, where $A_i$ is the area of part $i$ and $({\bar{x}}_i,{\bar{y}}_i)$ is the centroid of that part.

Notation: $\bar{x},\bar{y}$ = coordinates of centroid of composite, $A_i$ = area of part i.

An L-shaped area consists of two rectangles: Rectangle 1 is 6 m wide by 2 m tall with its bottom-left corner at the origin. Rectangle 2 is 4 m wide by 2 m tall, placed so its left edge is at x = 4 m and its bottom edge at y = 2 m (so it sits on top of and to the right of part of rectangle 1). All dimensions in meters.

Find:

Coordinates of the centroid of the composite area.

Centroid: $\bar{x}=2.6\text{m}$, $\bar{y}=1.8\text{m}$.