Question

A square is divided 16 Equal parts by intersecting lines parallel to its side .how many squares are formed in the resulting figure?

Answer 1

Given :  A square is divided in 16 Equal parts by intersecting lines parallel to its sides .

To Find : how many squares are formed in the resulting figure?

Solution:

Assume that given Square is 4 x 4 units

square is divided in 16 Equal parts by intersecting lines parallel to its sides .

Hence smallest square will be  1 x 1  sq unit

there will be 16 Squares of  1 x 1  units

there will be  9 square  of   2 x 2  units

there will be 4 square of  3 x 3  units

there will be  1 square  of 4 x 4  units  

Hence total number of square = 16 + 9 + 4 +  1  

= 30  

30 squares are formed in the resulting figure

( note : Direct/shortcut formula :  If divided into n x n  squares

then number of squares = n(n + 1) (2n + 1)/6

Here n = 4  =>  4(4+ 1) (2 * 4 + 1)/6  = 4 * 5 * 9 / 6 = 180/6 = 30 )

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