Question

The perimeter of a square is 36cm, Find its area.

Answer 1

Hint: We have to find the area of the square and we know that the given perimeter of a square is 36cm. First, we will assume the length of the side of the square as A, then using the formula for the perimeter of the square (4A)
We will get First, the value of A then using the formula for the area of for square (\[{{A}^{2}}\]) now putting the value of A in it we will get the value of the desired area of a square

Complete step-by-step solution:

We are given a square with its perimeter as 36cm and we are asked to find the value of the area of this square. Now if we assume the length of the square is A, now we know that square has 4 sides and all sides are equals, we know that the perimeter is the total boundary length of any structure so for square perimeter will be \[A+A+A+A=4A\], so equating it with 36 cm we get as
\[4A=36\] so, on solving we get the value of A as 9. Now to find the area of the square we apply formula \[{{A}^{2}}\]
So ion putting value \[A=9\] in \[{{A}^{2}}\] we get area equals to \[{{9}^{2}}\] which on solving we get as 81
Hence the area of the square is 81.

Note: If instead of the square we have a circle and its perimeter is given as 36cm and we have to find its area. then we area. use same above procedure but this time circle don’t have any side length so this time we will assume its radius as R, and perimeter formula is \[2\pi R\] and area formula is \[\pi {{R}^{2}}\]
So, on equating perimeter we get \[2\pi R=36\] on solving we get the value of R as 5.73 now its area will be \[\pi {{R}^{2}}=\pi {{(5.73)}^{2}}\] which on solving gives area equals to 103.09