The perimeter of the square was increased from 24 cm to 36 cm by how much the area of the square increased

All sides of a square are equal. This means that if the perimeter = 24 cm, then one side: 24: 4 = 6 (cm).
But the perimeter was increased to 36 cm. So, one side: 36: 4 = 9 (cm).
To find S (area), you need 9×9 = 81 (cm ^ 2). We are looking for the original S: 6×6 = 36 (cm ^ 2).
81-36 = 45 (cm)
Answer: S has increased by 45 cm