Area of Triangle: Find the Unknown Formula

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The discussion centers on finding the area of a triangle without using any known formulas for other shapes. Participants suggest using basic geometric manipulation, such as cutting and rearranging the triangle to form a rectangle, as a way to derive the area formula. There is an emphasis on utilizing vector and geometric concepts rather than relying on pre-existing area formulas. Some contributors also mention the importance of defining area to aid in the understanding of the problem. Overall, the conversation highlights the challenge of deriving the triangle area formula from fundamental principles.
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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