# Pythagorea Centroids 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 27.10 27.11 27.12 27.13 27.14 27.15 27.16 27.17 Solution

Pythagorea Centroid all levels solved here. Pythagorea is an android/iOS app developed by Horis International Limited. Solutions hints and answers to pythagorea are available in this post scroll down to find solutions to all the levels. This game is mostly focused on geometric puzzles and construction. The work space is divided into grids to draw lines. You should know all the basic Math operations. All lines and shapes are drawn on a grid whose cells are squares. Most of the game levels can be answered using natural intuition and by some basic laws of geometry.

**Download link for Android devices:** https://play.google.com/store/apps/details?id=com.hil_hk.pythagorea

**Download link for iOS devices:** https://itunes.apple.com/us/app/pythagorea-geometry-on-square-grid/

If you are here for levels other than

‘Centroids’Go to directory of all other levels at : https://www.puzzlegamemaster.com/pythagorea-all-answers-solutions/

## Pythagorea Centroids All Levels (Click on required level)

- Pythagorea Level 27.1 Answer Solution [Centroids]
- Pythagorea Level 27.2 Answer Solution [Centroids]
- Pythagorea Level 27.3 Answer Solution [Centroids]
- Pythagorea Level 27.4 Answer Solution [Centroids]
- Pythagorea Level 27.5 Answer Solution [Centroids]
- Pythagorea Level 27.6 Answer Solution [Centroids]
- Pythagorea Level 27.7 Answer Solution [Centroids]
- Pythagorea Level 27.8 Answer Solution [Centroids]
- Pythagorea Level 27.9 Answer Solution [Centroids]
- Pythagorea Level 27.10 Answer Solution [Centroids]
- Pythagorea Level 27.10 Answer Solution [Centroids]
- Pythagorea Level 27.12 Answer Solution [Centroids]
- Pythagorea Level 27.13 Answer Solution [Centroids]
- Pythagorea Level 27.14 Answer Solution [Centroids]
- Pythagorea Level 27.15 Answer Solution [Centroids]
- Pythagorea Level 27.16 Answer Solution [Centroids]
- Pythagorea Level 27.17 Answer Solution [Centroids]

Video link for further hints:

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There is a common solution to all ” Centroids” … it is basically more calculus than geometry ..

the formula is “SUM of the Areas multiplied by the corresponding Y- or X-coordinate” divided by the “SUM of the Areas”… in this case there are two shapes (n=1 and n=2), then…

n Yn Area n Area n * Yn Xn Area n Area n * Xn

———————————————————————————————–

1 4 (6*3/2)=9 9*4=36 1 9 9

2 2.5 (3*3)=9 9*2.5=22,5 4,5 9 40,5

————————————————————————————————-

Yn = (36+22,5)/(9+9) = 3,25 Xn = (9+40,5)/(9+9) = 2,75

and the Center of gravity / common centroid with these coordinates can easily be constructed

(for more than two shapes just add the corresponding n-lines)

27.14 has a simple solution than this sorcery!

Please share

27.13 has a much simpler solution. The two parallelograms have an area of 4 and 6 square units respectively, Hence the centroid lies on the line joining the respective centroids of the two figures. It will divide the line in the ratio of the two areas viz 3:2 (it lies closer to the figure with the greater area). Since it all boils down to dividing the segment joining the two centroids in the ratio of the two areas, we proceed as follows:

(a) Locate the centroids of the two parallelograms and connect them by a straight line (we call it line A).

(b) Draw a vertical line 5 units long starting from the centroid of the upper parallelogram (line B). Draw a line connecting the free end of line B to the centroid of the lower parallelogram (let this be called line C). Locate on line B, a point 3 units from its top. Call this point O.

c) Thru O draw a line parallel to the line C. Then the desired centroid is the point where this parallel line intersects Line A.

Step 2 is redundant.

If you were to

A connect the centroid.

Take 1 unit off from parallelogram B at point o diagonally up right. Logic is again centroid has to divide area equally….

The 27.9 solution is false