Perimeter of Rectangle and Square:
The perimeter of a shape is the distance around the shape. For a rectangle, the perimeter is calculated by adding the lengths of all four sides. Similarly, for a square, the perimeter is the sum of all four equal sides.

Given Information:
We are given that the perimeter of a rectangle is 72 cm.

Solution:
To find the area of the square, we need to have some relation between the rectangle and the square.

Perimeter of Rectangle:
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)

Given that the perimeter of the rectangle is 72 cm, we can write the equation as:
72 = 2 * (Length + Width) ----(1)

Perimeter of Square:
The perimeter of a square is given by the formula:
Perimeter = 4 * Side

Let's assume the side of the square is 's'. Therefore, the equation for the perimeter of the square can be written as:
Perimeter = 4s ----(2)

Since the perimeter of the rectangle and the square is equal, we can equate equations (1) and (2):
2 * (Length + Width) = 4s

Dividing both sides of the equation by 2, we get:
Length + Width = 2s ----(3)

Finding the Area of the Square:
The area of a square is given by the formula:
Area = Side * Side

Since all sides of a square are equal, we can write the equation for the area of the square as:
Area = s * s
Area = s²

We need to find the value of 's²' or the area of the square.

Using equation (3), we can substitute '2s' for 'Length + Width':
Length + Width = 2s

Since we know the perimeter of the rectangle is 72 cm, we can rewrite the equation as:
72 = 2s

Dividing both sides of the equation by 2, we get:
36 = s

Now, substituting the value of 's' in the equation for the area of the square:
Area = s²
Area = (36)²
Area = 36 * 36
Area = 1296 cm²

Therefore, the area of the square is 1296 cm², which is the same as option A.

4a=2(l+b) then 2(l+b)=72
4a=72 then a=72÷4=18
area of square =side×side

=18×18


=324 cm2
option a