Question

How do I find the perimeter of a square from the area of the square?

Answer 1

Perimeter`=4×sqrt(Area`

Explanation:

It's quite easy to find the perimeter of a square if you know it's area. It goes as follows :-
Suppose the side of the square you have is `s` and let the area be `a`
We know that the formula for the area of a square is `side^2`
Area `=side^2`
`:. a` = `s^2`
`:. s = sqrta`
So we will obtain the side of the square.
Now we know that the formula for the perimeter of a square is `4 ×` side.
`:.` Perimeter `= 4 × s`
`:.` Perimeter `= 4 × sqrta`

Answer 2

`"Perimeter" = 4\sqrt("Area")`

Explanation:

If the side of the square was `x` the area would be `x^2`.

Therefore, if you knew what the area was, you can square root the value to get the length of one side, as `\sqrt(x^2) = x = \sqrt("Area")`.

Here, we ignore the negative value of the square root as lengths cannot be negative.

Since the perimeter of the square is equal to `4x` you can substitute `x` with `\sqrt("Area")` and get:

`"Perimeter" = 4\sqrt("Area")`

Hope that makes sense!