Change a Pentagon into a Triangle with Equal Area

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Discussion Overview

The discussion revolves around the problem of transforming a pentagon into a triangle while maintaining equal area. Participants explore various assumptions and methods related to this geometric transformation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant proposes constructing a triangle APQ from a pentagon ABCDE such that both shapes have the same area.
  • Some participants question whether the pentagon is assumed to be regular, with one noting that it may not necessarily be regular.
  • Another participant suggests splitting the pentagon into three triangles and mentions using the formula \displaystyle \frac{1}{2}ab\sin{(C)} to find the area of each triangle.
  • A request is made for a diagram to clarify the problem, with a promise to upload a visual representation later.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the assumptions about the pentagon's regularity, and there is no consensus on the method for achieving the area transformation.

Contextual Notes

There are limitations regarding the assumptions about the shape of the pentagon and the methods proposed for calculating areas, which remain unresolved.

Albert1
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ABCDE is a pentagon,now please construct a triangle APQ
,and both of them must have the same area
 
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Re: change the shape of a pentagon into a triangle with equal area

Are we assuming this is a regular pentagon?
 
Re: change the shape of a pentagon into a triangle with equal area

Prove It said:
Are we assuming this is a regular pentagon?
it may not be a regular pentagon
 
Well I would be inclined to split the pentagon into three triangles, you should be able to find the area of each triangle using \displaystyle \begin{align*} \frac{1}{2}ab\sin{(C)} \end{align*} or some other method...
 
Hope you can upload a diagram ,so we can see it clearly
,I will upload mine later
 

Attachments

  • pentagon.jpg
    pentagon.jpg
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