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Why is this concept useful?: The analysis of distributed forces, the analysis of bending in beams, the analysis of torsion in shafts, and as an intermediary step in calculating moments of inertia are all circumstances where centroids of areas are important in the mechanics course sequence.
Where does this concept fit into the curriculum?: High School

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How to Use Centroid:

A centroid is the midpoint of a triangle
You can calculate the centroid of a triangle by its medians
A triangle has 3 medians

In this model it shows that every vertex is ⅔ away from the centroid and the median is ⅓ away from the centroid

Sample Math Problems

Question

P is the centroid of △ABC. BE = 11, AP = 10, BP = 8

Find the length of segment EC.

Solution

BE = 11, that is half of BC.
Answer: EC = 11 units.

Question

P is the centroid of △ABC. BE = 11, AP = 10, BP = 8

Find the length of segment AE.

Solution

AP is ⅔ of AE.
AP = 10. 10 x 3/2 = 15
Answer: AE is 15 units.

Question

P is the centroid of △ABC. BE = 11, AP = 10, BP = 8

Find the length of segment PF.

Solution

BP = 8. BP is also ⅔ of BF.
8 x 3/2 = 12/3 = 4
Answer: PF = 4 units.

Question

P is the centroid of △ABC. BE = 11, AP = 10, BP = 8

Find the length of segment BF.

Solution

BP = 8. 8 x 3/2 = 12
Answer: BF = 12 units.

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