Question

How do I find the perimeter of a square if I know its area?

Answer 1

Hint: First determine the side of the square with the help of the given perimeter. Since all the sides in a square are the same, the formula for its perimeter is \[P = 4s\] ,where \[s\] is the side of the square. Then apply the formula for the area of the square i.e. \[A = {s^2}\] to get the answer.

Complete step-by-step answer:
According to the question, let us assume the perimeter of the given square is \[s\] units.
We know that in a square, all four sides are of equal length. Hence the formula for the perimeter of the square is -
\[ \Rightarrow P = 4s\], where \[s\] is the side of the square.
Applying this formula for the given perimeter, we’ll get:
\[ \Rightarrow 4s = P\] \[ \Rightarrow s = \dfrac{P}{4}\]
Thus the side of the square is of \[\dfrac{P}{4}\] units length.
Now, we have to calculate the area of the square. We also know that the formula to determine the area of the square is \[A = {s^2}\] .
Applying this formula and putting the value of \[s\] i.e. side length of the square from perimeter formula we get as follows \[ \Rightarrow A = {s^2} = {\left( {\dfrac{P}{4}} \right)^2} = \dfrac{{{P^2}}}{{16}}\]
Therefore the area of the given square is \[\dfrac{{{P^2}}}{{16}}\] \[{\text{unit}}{{\text{s}}^2}\].

Note: All the angles in a square are of \[90^\circ \]. If all the sides of a quadrilateral are not equal but opposite sides are parallel and equal instead, along with all the angles \[90^\circ \] then the quadrilateral is called a rectangle. The perimeter of a rectangle is given by the formula \[P = 2\left( {l + b} \right)\] whereas its area is calculated by the formula \[A = l \times b\], where \[l\] is the length and \[b\] is the breadth of the rectangle.