How does the area of a square change if its 6 cm side is reduced by 2 cm? How will the perimeter of the square change?

The area (S) and perimeter (P) of a square are calculated using the formulas:

S = l × l;

P = l × 4;

where l is the length of the side of the square.

Find the area and perimeter of the original square:

S1 = 6 × 6 = 36 cm2;

Р1 = 6 × 4 = 24 cm;

The side length of the new square will be:

l2 = 6 – 2 = 4 cm;

Find the area and perimeter of the new square:

S2 = 4 × 4 = 16 cm2;

P2 = 4 × 4 = 16 cm;

Let’s find how the area and perimeter of the square will change:

∆S = S1 – S2 = 36 -16 = 20 cm2;

∆Р = Р1 – Р2 = 24 – 16 = 8 cm.

Answer: the area of the square will decrease by 20 cm2, the perimeter will decrease by 8 cm.