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Discussion Overview

The discussion revolves around a visual puzzle involving shapes that are purported to be triangles. Participants are analyzing the areas of these shapes and questioning their geometric properties, focusing on the apparent contradictions in area calculations and the nature of the shapes involved.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the shapes in the puzzle are actually triangles, suggesting a careful examination of their intersections and slopes.
  • Another participant calculates the area of the whole "triangle" as 32.5 but finds a discrepancy when summing the areas of the individual pieces, leading to a suspicion that the shapes may not be triangles.
  • A different participant identifies the small dark green shape as a right triangle with legs 2 and 5, and the large red shape as a right triangle with legs 3 and 8, asserting that they are not congruent.
  • One participant expresses satisfaction with their answer, implying they believe their reasoning is correct.
  • There is a technical note regarding the visibility of an attached image, indicating that it must be accessed through a link rather than being displayed directly.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are competing views regarding the nature of the shapes and the validity of the area calculations. Some participants express confidence in their interpretations, while others challenge the assumptions made about the shapes.

Contextual Notes

There are unresolved assumptions regarding the geometric properties of the shapes and the implications of the area calculations. The discussion relies on visual elements that are not universally accessible to all participants.

ermines
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Help... (illusion)

could someone figure out the answer...
 

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...excuse me, but why can't i see the .gif i attached...
 
Are either of those shapes actually triangles? Look carefully at the intersection of the diagonal with the grid. Or calculate the slopes of the diagonal lines.
 
I think Damgo is right.

If you calculate the area of the whole "triangle" you get:

Area = (1/2)*(13*5) = 32.5

However if you calculate the area of each individual piece you get:

Red: = (1/2)*(8*3) = 12
Light Green: = 8
Dark Green: = (1/2)*(5*2) = 5
Yellow: = 7

Adding these values up we get a total area of 32.

There is a contradiction here, therefore there is something fishy going on, and I think it has to do with the assumption that the apparent triangles are truly triangles.
 
The four shapes do not come together to make a triangle. The small triangle (dark green) is a right triangle with legs 2 and 5; the large triangle (red) is a right triangle with legs 3 and 8. They are not congruent.

P.S.: You cannot see the attached image because it is an attachment. Veiw the attachment by selecting the link. If you want to insert an image, you will have to use IMG tags. https://www.physicsforums.com/misc.php?action=bbcode#imgcode
 
Last edited by a moderator:
so my answer was right, yehey...
 

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