What’s an injective function?
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You problem is you don't have any problem. You have a bunch of formulas for the perimeter and area of some shapes.
As for using the formulas, usually you're given all but one of the variables and you can solve for the remaining one.
Notice how the triangle result doesn't have area as a function of a, b and c. That's called Heron's formula and is usually not taught to secondary school students. I don't like to teach it either because Archimedes' Theorem is so much better:
The sides a,b,c and area S of a triangle satisfy