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

2 Answers

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#

Mar 21, 2018

#"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!