I'm given a unit cube. The task is to find the perimeter of triangle ACE. I have no other information, but considering it's a unit cube that should be more than enough.
Am I looking for an answer like this by any chance?
Anyways, cheers!
How do I go about calculating the perimeter of a triangle that consists of three vertices of a cube?
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4That would be unnecessary. You just need to apply Pythagoreas' Theorem multiple times. – player3236 Feb 02 '21 at 19:55
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1What are $A, C$ and $E$? – Gribouillis Feb 02 '21 at 20:27
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1In this wikipedia page there is a formula for the area of a general triangle in ${\mathbb R}^3$ given the verctices' $3$-dimensional coordinates. – Gribouillis Feb 02 '21 at 20:32
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1@user2661923 Thanks. Apparently I misread the question. – Gribouillis Feb 02 '21 at 22:20
1 Answers
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The question would have been more specific if the annotation of the vertices were given.
So, the edges of the triangle can either be 1. a surface diagonal i.e., the diagonal connecting the running along the surface of the cube, 2. a body diagonal i.e., the diagonal connecting the vertices at opposite ends of the cube 3. an edge.
Egde = a = 1
surface diagonal = s = $\sqrt{a^2 + a^2}$ = $\sqrt{1^1 + 1^1}$ = $\sqrt{2}$
body diagonal =$ \sqrt{a^2 + s^2} = \sqrt{1^2 + 2} = \sqrt{3}$
see which of these three are the edges of your triangle and add them.
aditya singh
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