Area of Triangle: Find the Unknown Formula

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Homework Help Overview

The discussion revolves around finding the area of a triangle without using known formulas for other geometric figures. Participants are exploring the foundational understanding of how the area of a triangle can be derived from basic principles, particularly focusing on the constraints of not using other area formulas.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants suggest manipulating the triangle into a rectangle to visualize the area. Others question the necessity of knowing the area of a rectangle and propose using vector and geometric manipulation instead. There are also inquiries about the initial formulation of the area of a triangle.

Discussion Status

The discussion is active, with various approaches being suggested. Some participants are providing hints and guidance on how to think about the problem, while others are seeking clarification on the methods proposed. There is no explicit consensus on a single approach yet.

Contextual Notes

Participants are constrained by the requirement to not use any known area formulas, which is leading to a focus on basic calculus and geometric reasoning. There is also a mention of needing to make an attempt before asking for help, reflecting the forum's rules on engagement.

subhradeep mahata
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Homework Statement


Find the area of a triangle, assume that you don't know the formula of area of any other figure.

Homework Equations

The Attempt at a Solution


Well, i was trying to figure out how to find the area of a triangle out of nowhere, but could not get it. I want to know how it was formulated for the very first time. Please help me out (remember that you cannot use any other area formula) . You can use basic calculus, but not very advanced one.
 
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Can you cut the triangle and arrange the pieces so they make a rectangle?
 
Please show me how to do it.
 
subhradeep mahata said:
Please show me how to do it.
PF rules require YOU to make an attempt first, before asking for help.
 
subhradeep mahata said:

Homework Statement


Find the area of a triangle, assume that you don't know the formula of area of any other figure.
Not even the area of a rectangle?
 
Try using box method of area
 
subhradeep mahata said:

Homework Statement


Find the area of a triangle, assume that you don't know the formula of area of any other figure.

Homework Equations

The Attempt at a Solution


Well, i was trying to figure out how to find the area of a triangle out of nowhere, but could not get it. I want to know how it was formulated for the very first time. Please help me out (remember that you cannot use any other area formula) . You can use basic calculus, but not very advanced one.
Wrong requirement. USE knowledge of area of a rectangle! This will let you form a diagram like a construction to develop formula for area of a triangle.
 
You don't need to know anything else, just VECTOR and GEOMETRIC manipulation will suffice.

Capitalised are hints.

Thanks.
 
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subhradeep mahata said:
Find the area of a triangle, assume that you don't know the formula of area of any other figure.
Well, you can know the fromula of a triangle since it isn't any other figure.:wink:
 
  • #10
Start by defining area, I think that may lead to answer.
 

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