Page 239 - Ganit Kaushal

2. Squares with a Hole

Construction 19: Construct a square with a side length of 4 cm and a circular hole at the centre
of the square, as shown in the adjoining figure. (NCERT)

Sol. Follow the given steps:
Step 1: Draw a square ABCD of side length 4 cm, as explained in construction 5 (see A 4 cm B
figure (i)).
Step 2: We know that the centre of a square is the point of intersection of its diagonals. 4 cm
Draw the diagonals of the square. Let them intersect at point O (see figure (ii)). D C
(i)
Step 3: With O as the centre and using a radius of any length less A 4 cm B A 4 cm B
than 2 cm, (say 1.5 cm) for construction, draw a circle. To get the
final figure (iii), remove all the supporting lines and points. O 4 cm 4 cm

3. Squares with More than One Hole D C D C
(ii) (iii)
Construction 20: Construct a square. Divide it into four squares and four circular holes at the
centre of each square, as shown in the adjacent figure. (NCERT)

Sol. Follow the given steps:
Step 1: Draw a square ABCD of side length 8 cm. Mark the midpoint of each side as P,
Q, R, and S, using a ruler. Join P and R, S and Q. This way, the outer square ABCD will
be divided into 4 smaller squares, with a side length of 4 cm each. Draw the diagonals by joining the
opposite corners of each of these smaller squares. A P B A B
Mark the points of intersection of these diagonals
as E, F, G, and H as shown in the figure (i). E F
Step 2: The points E, F, G, and H are the centres of S Q
the circular holes. Take the radius of each circular
hole as 1.5 cm. Draw four full circles with centres H G
at E, F, G, and H. Remove all the supporting lines D C D C
R
and points to get the final figure, as shown in (i) (ii)
figure (ii).

4. Falling Squares

Construction 21: Construct a set of three squares with side length 4 cm each, aligned 4 cm
diagonally to each other, as shown in the figure. (NCERT)
4 cm

4 cm
Each is a square
of side 4 cm
Sol. Follow the given steps:
4 cm
Step 1: Construct a square with a side length of 4 cm, as explained in construction 5 A B
(see figure (i)).
Step 2: Extend the side AB up to point E such that AE = 8 cm. Similarly, extend the
side CB up to point F such that CF = 8 cm, using a ruler and pencil. D C
(i)

Playing with Constructions 237