Question

A square sheet of 8cm side was taken and made into 64 equal small squares. Find the perimeter of
square sheet and also find the sum of the perimeters of all 64 small squares. What did you observe?​

Answer 1

Side = 8cm

perimeter of square sheet = 4×side

= 4×8cm = 32cm

and, area of square sheet = (side)²

= (8cm)² = 64cm²

Area of 64 small squares =64cm²

Area of 1 small square = 1cm²

side of 1 small square= √1cm²

= 1cm

and, perimeter of small square = 4×side

= 4× 1cm = 4cm

perimeter of all small squares = 4cm×64

= 256cm

we observed that the perimeter of sum of all perimeter of all small squares is greater than perimeter of square sheet.