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Similarly, by cutting the line l three times, we can draw a rectangle that can be divided in three
identical squares.

A′ P′ Q′ B′

l
A P Q B
Example 5: Construct the falling squares given below in the same way they are aligned.

2 cm
4 cm

6 cm

Solution: Draw a square of side 2 cm.
2 cm

Next, produce the base of the first square and Similarly, draw a square of side 6 cm at one
draw a square of side 4 cm at one corner of the corner of the second square.
previous square. 2 cm
2 cm 4 cm

4 cm
6 cm

Shading the Square

Let the side of a square be 16 cm. Join the midpoints of the sides of this square to form a new
square and four triangles. Shade one triangle and continue the process as shown below.

16 cm

Repeat the process up to 5 times to get a shady region in a square.

241 Playing with Constructions