Question on square area

Consider a 6 × 7 grid of unit squares as shown in the fig


(i) How many rectangles are the union of one or more of the unit squares of
the grid? (A 1 × 1 square counts as a rectangle.)

(ii) How many of the squares are in the figure?

(iii) What is the sum of the area of all the squares?

(iv) How many squares have a perimeter that is more than 8 unit?

(v) How many of the rectangles have area 12?

(vi) How many of the rectangles are the union of an odd number unit squares?

(vii) How many of the rectangles have a perimeter that is a multiple of 3?    

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Submitted by srikant on Wed, 2008-05-07 23:08.