Calculating the Centroid Position of a Symmetrical T-Section

[mechanicstudy]

Basically for the last three hours I have been struggling with this question.

"Calculate the position of the centroid of a symmeterical t-section having a vertical stem 40mm wide by 120mm high, and a top section which is 80mm wide and 40mm high."

The answer is meant to be 92mm but I have no idea how this was achieved. I tried splitting it into two rectangles but there isn't a way for me to draw a line to find the centroid. I then try to get the areas of each block but the formulas are just confusing.

Can anyone help me?

Thanks!

 

[PhanthomJay]

When finding the centroid of an area in relation to an axis, you sum moment areas of each area about a convenient axis, then divide by the total area. The moment arm of each area is the distance from the centroid of that area to the axis. The formula and word description of that formula can look and sound confusing. Split the section into 2 areas and choose the bottom of the vertical stem as the convenient reference axis. I will do the top moment area calculation for you...(80)(40)(120 + 20) = 448000 . Now do a similar calc for the stem section, add em up, and divide by the total area of both sections to get the distance of the centroid from the bottom reference axis.