Part A

All real-world triangles have a single point called the center of mass.This point represents the average position of all of the triangle's mass.So, in theory, any triangle can balance with a force applied only to its center of mass.A pencil tip, for instance, could hold up a real-world triangle if it were placed directly at the triangle's center of mass.

Consider what you know about the three points of concurrency mentioned above, or conduct outside research, if necessary.One of these triangle centers always occurs at a triangle's center of mass.Which point of concurrency is it?Explain your reasoning.

Part C

Suppose a steel triangle is cut by a machinist who's helping to build a bridge.The triangle is cut with the dimensions of triangleABC in units of meters.The triangle has a uniform thickness of 0.8 meters.So the triangle is in the shape of a right triangular prism.Describe the location of this triangle's center of mass, which will still be a single point.Explain your answer.

Part D

After cutting the triangle, the machinist learns that he needs to cut a cross section of it along the median running through pointBand the midpoint of sideAC.What will the area of this cross section be?