Q. 3

# See this pictures

i) How many small squares are there in each rectangle?

No. of small squares in

Rectangle 1 - 2

Rectangle 2 - 4

Rectangle 3 - 6

Rectangle 4 - 8

As is evident, it forms an AP with common difference = 4-2 =2

ii) How many large squares?

No. of large squares in

Rectangle 1 - 0

Rectangle 2 - 1 (intersection of all 4 small squares)

Rectangle 3 - 2 (2 same size overlapping squares as in rectangle 2)

Rectangle 4 - 3

As is evident, it forms an AP with common difference = 1-0 =1

iii) How many squares in all?

All squares = small squares + large squares

No. of all squares in

Rectangle 1 - 2 + 0 = 2

Rectangle 2 - 4 + 1 = 5

Rectangle 3 - 6 + 2 = 8

Rectangle 4 - 8 + 3 = 11

As is evident, it forms an AP with common difference = 2+1 = 3

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