[Math] Center of volume and volume for triangle wedge

centroidgeometryvolume

Let's say we have a wedge, where the base is a triangle, parallel with the $xy$-plane, and where only one of the sides extends perpendicular to the base:

Perspective view of triangle wedge

Here is the same wedge, looking down the Z-axis:

enter image description here

We know:

  • The vertices of the triangle, $B$, $L$ and $R$
  • The height $h$ of the extending side
  • Then also the base area $A$ and centroid $C$, I'm sure

Questions

  • How can we calculate the volume of the wedge?
  • How can we calculate the center of volume, $C_{V}$?

PS. I'm a layman at math. Sorry if this is overly trivial, badly worded or inappropriate.

Best Answer

For the volume:

$$V=\frac13 A\cdot h$$

For the centroid, denote with U the up vertex, by vectors:

$$C_v={B+L+R+U\over 4}$$

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