Perimeter of Rectangle and Square:

The perimeter of a rectangle is the sum of all its sides. In this case, the rectangle has a length of 20 cm and a breadth of 16 cm. Therefore, the perimeter of the rectangle can be calculated as follows:

Perimeter of Rectangle = 2 × (Length + Breadth)
= 2 × (20 cm + 16 cm)
= 2 × 36 cm
= 72 cm

Since the perimeter of a square is the sum of all its sides as well, and the perimeter of the rectangle is equal to the perimeter of the square, we can calculate the length of the sides of the square.

Perimeter of Square = 4 × Side

Since the perimeter of the square is equal to 72 cm, we can write the equation as:

4 × Side = 72 cm

By dividing both sides of the equation by 4, we can find the length of one side of the square:

Side = 72 cm / 4
= 18 cm

Area of Rectangle and Square:

The area of a rectangle is calculated by multiplying its length and breadth. In this case, the area of the rectangle can be calculated as follows:

Area of Rectangle = Length × Breadth
= 20 cm × 16 cm
= 320 cm²

The area of a square is calculated by multiplying the length of one side by itself. In this case, the area of the square can be calculated as follows:

Area of Square = Side × Side
= 18 cm × 18 cm
= 324 cm²

Difference between Area of Rectangle and Square:

To find the difference between the area of the rectangle and the square, we subtract the area of the square from the area of the rectangle:

Difference = Area of Rectangle - Area of Square
= 320 cm² - 324 cm²
= -4 cm²

Therefore, the difference between the area of the rectangle and the square is -4 cm². However, since area cannot be negative, we take the absolute value of the difference:

|Difference| = |-4 cm²|
= 4 cm²

Hence, the correct answer is option B: 4 cm².