The answer will depend on a segment of WHAT. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
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The answer will depend on what the formula is for: the perimeter or area of the segment.
No because the formula for finding the area of an oval, which is an ellipse, is quite different
The answer depends on the formula for what: the radius, circumference, length of an arc, area, area of sector, area of segment: each one has a different formula.
Squares are rectangles so the formula for area will stay the same.
the formula depends on the shape of the object