Understanding the Square Fields

We are given information about two square fields, let's call them Field A and Field B. We need to find the area of Field B.

Calculating the Side of Field A

Let the side length of square Field A be represented by the variable '$a$'.

The perimeter of a square is calculated by the formula: Perimeter = 4 × side.

So, the perimeter of Field A is $4a$ cm.

The problem states that the difference between the perimeter of Field A and its side is 48 cm.

We can write this as an equation:

Perimeter of A - Side of A = 48

Substituting the formula for the perimeter:

$$4a - a = 48$$

Now, we simplify the equation:

$$3a = 48$$

To find the side '$a$', we divide both sides by 3:

$$a = \frac{48}{3}$$

$$a = 16$$

Therefore, the side length of square Field A is 16 cm.

Calculating the Side of Field B

The problem states that the side of square Field B is 4 cm less than the side of square Field A.

Let the side length of square Field B be represented by the variable '$b$'.

Using the side length of Field A ($a = 16$ cm), we can find '$b$':

$$b = a - 4$$

$$b = 16 - 4$$

$$b = 12$$

So, the side length of square Field B is 12 cm.

Calculating the Area of Field B

The area of a square is calculated by the formula: Area = side × side or Area = side$^2$.

We need to find the area of square Field B, which has a side length '$b$' of 12 cm.

Area of Field B = $b^2$

Area of Field B = $12^2$

Area of Field B = $12 \times 12$

Area of Field B = 144

The area is measured in square centimeters (cm$^2$).

Thus, the area of square Field B is 144 cm$^2$.