Triangle Area Homework Statement | Image for Reference

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The area of a triangle can be calculated using the formula A = 1/2 bh, where b is the base and h is the height. When considering a fixed base AB, if the area remains constant, the height must also remain constant, meaning point C must move along a line parallel to AB. The discussion highlights the importance of clearly stating the problem in text rather than relying on images for clarity. The cross-product method for finding the area was deemed unnecessary for this context. Overall, the participants reached an understanding of the relationship between the triangle's area, base, and height.
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Homework Statement


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I don't know where to start.
 
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What is the formula for the area of a triangle, if one is given base and height?

Has one done the cross product of two vectors?
 
Astronuc said:
What is the formula for the area of a triangle, if one is given base and height?

Has one done the cross product of two vectors?
(1/2)b*h

I haven't done the cross-product but it's preparation for the ACT, so there must be another way to do it.
 
Nevermind the cross-product. I was thinking that you had to find the area of the triangle. In future, please write out the problem statement in the post, rather than leaving it as a image.

Anyway, so we have A = 1/2 bh, as the area. Now if we take the line segment AB as the base, b, which is fixed, then what does h represent with respect to point C? And if the area, A, and base, b, remain constant, what does that imply about point C with respect to line segment AB?
 
Take AB as the base. As C moves, A and B stay fixed so b stays constant. In order that the area be constant, h must also be constant. That means C must move along a line parallel to AB.
 
Astronuc said:
Nevermind the cross-product. I was thinking that you had to find the area of the triangle. In future, please write out the problem statement in the post, rather than leaving it as a image.

Anyway, so we have A = 1/2 bh, as the area. Now if we take the line segment AB as the base, b, which is fixed, then what does h represent with respect to point C? And if the area, A, and base, b, remain constant, what does that imply about point C with respect to line segment AB?

HallsofIvy said:
Take AB as the base. As C moves, A and B stay fixed so b stays constant. In order that the area be constant, h must also be constant. That means C must move along a line parallel to AB.
Alright, I get it now. Thank you both for the help.

Astronuc, sorry about that. I'll write out the question next time.
 

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