Geometry Worksheets

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Centroid

By Puja Varude

The place where the three medians meet is the triangle's centroid. According to the centroid theorem, the centroid is 2/3 times the distance between each vertex and the opposing side's midpoint.

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

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

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

Question

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

Find the length of segment AE.

Solution

  1. AP is ⅔ of AE.
  2. AP = 10. 10 x 3/2 = 15
  3. 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

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

Question

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

Find the length of segment BF.

Solution

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

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Practice Math Problems

1. F is the centroid of △ZYX. FU = 6, ZX = 20, WX = 15.

Find the length of segment YU.

2. F is the centroid of △ZYX. FU = 6, ZX = 20, WX = 15.

Find the length of segment UX.

3. F is the centroid of △ZYX. FU = 6, ZX = 20, WX = 15.

Find the length of segment FX.

4. F is the centroid of △ZYX. FU = 6, ZX = 20, WX = 15.

Find the length of segment YF.

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