Question

Find the perimeter of a square whose area is \[1.69\text{ }{{\text{m}}^{2}}\].

Answer 1

Hint: we will make use of the formulas for squares known to us.
We have been given the area of the square. We know the formula for the area of a square and through this area given to us, we will find the length of the side of a square.
From the length of the side we found out, we can find the perimeter through the formula.
Formula used:

\[\begin{gathered}
  & A={{a}^{2}} \\
 & P=4a \\
\end{gathered}\]
The formula for area of a square and the formula for the perimeter of a square are mentioned above.

Complete step by step solution:
we will make use of the area given to us and through that find the side and find the perimeter.
The given area being:
\[\begin{gathered}
  & A={{a}^{2}} \\
 & A=1.69\text{ }{{\text{m}}^{2}} \\
 & \text{or, }{{a}^{2}}=1.69\text{ }\!\![\!\!\text{ }\because A={{a}^{2}}\text{ }\!\!]\!\!\text{ } \\
 & a=\sqrt{1.69} \\
 & a=1.3\text{ m} \\
\end{gathered}\]
Since we have the value of side length we can find the perimeter of the square.
Therefore, the perimeter of square through formula:
\[\begin{gathered}
  & p=4a \\
 & p=4\times 1.3 \\
 & p=5.2\text{ m} \\
\end{gathered}\]
Perimeter of the square is 5.2 m.

Additional Information: Square is a quadrilateral whose sides are equal. The area of a quadrilateral is side multiplied by side whereas, the perimeter is side + side + side + side.

Note: Area of 2D figures are measured in square units. Therefore, \[{{\text{m}}^{2}}\] is a square meter used for measurement of area. ‘\[\text{m}\]’ is meter in unit length. Take extra note while calculating the value of length through the area given. Since the length of each side came in radical form.‘P’ is for perimeter and ‘A’ is for the area.
 The area was\[A=\text{length}\times \text{breadth=}a\times a\]. Whereas, the perimeter is similar to the fencing.