Engineering Statics Center of Gravity Problem

[ttran1117]

Homework Statement

For the machine element shown, locate the x coordinate of the center of gravity.
The picture of 2 different problems are attached

Homework Equations

V = 1/3*a*b*h

The Attempt at a Solution

I can figure out the coordinates fine for everything except the triangles. I looked at the solution for problem 96 and I can't seem to figure out why the solution is 2/3*66 + 34 (coordinate). I understand that the base would be x/3, or 66/3, which is true for problem 98, so why isn't it problem 96 using 34+ 1/3*66 and instead is using 34 +2/3*66? Any help would be greatly appreciated, as I have spent a long time on this and can't seem to figure it out. Also, would this be same for the y component as well? Thank you very much

 

[pongo38]

I think the triangle you speak of is the 'empty' triangle in the xz plane. What is the x-coordinate of its centre of gravity? To check this, draw a plan of the triangle and obtain the position of G by joining the mid point of each side to its opposite corner. Hopefully this is enough for the penny to drop.