Correct spelling, explanation: the noun perimeter comes from Latin perimetros and from Ancient Greek perímetros. It’s also an equivalent to peri- +‎ meter. As you can see, it has a long history. You can’t change its construction, so perameter is an incorrect version. If you’re not sure how to write a word, always look at its etymology. It will be easier for you to remember the spelling if you know what the prefix peri- means – around, about, enclosing.

Definition of perimeter:
noun, the distance around the edge of a shape
The river marks the eastern perimeter of our land.
Guards patrolled the perimeter fence.

Collocations with perimeter:
Some most commonly used collocations include: on the perimeter and along the perimeter.
There’s a small shop on the perimeter of the camp.
I lugged my suitcase along the perimeter of the square.

Incorrect spelling, explanation: we shouldn’t spell this word as perameter because its first part doesn’t accord with the dictionary version, so the noun loses its meaning. The correct version consists of two elements: the prefix peri- and the word meter. Peri- comes from the Greek language and it’s a word-forming element meaning around, about, enclosing. That’s why perimeter is the only right spelling.