Yes in equilateral triangle.
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A circle !!!!!!
It could be a right angle triangle
It could be but does not have to be... (Perpendicular to what?)
A traingle covers half the area of a rectangle with the same base and [perpendicular] height.
An equilateral quadrilateral is not a well defined shape - it could be a rhombus with one angle able to take ANY value. In the same way, an equilateral dodecagon is not a well defined shape and so it is impossible to give a sensible answer to the question.