Page 240 - Ganit Kaushal

Step 3: Draw a perpendicular to line BF I 4 cm J
at F and a perpendicular to line BE at E
with the help of a protractor. They cut
each other at G (see figure (ii)). 4 cm 4 cm G
Step 4: Extend the side FG up to point F G F H
H such that FH = 8 cm. Extend the side
EG up to point I such that EI = 8 cm,
using a ruler and pencil. A 4 cm B E A 4 cm B E
Step 5: Draw a perpendicular to line EI
at point I and draw another perpendicular
to line FH at point H with the help of a D C D C
protractor. They cut each other at J. This (ii) (iii)
gives us the final required figure (iii).

5. Four-Sided Figure but not a Square

Construction 22: Construct a 4-sided figure in which all sides are equal to 5 cm, but it is not a square. (NCERT)

Sol. Follow the given steps:
Step 1: Draw a line AB, 5 cm long, with the help of a ruler and a pencil (see figure (i)). A 5 cm B
Step 2: Draw another line AD at point A, 5 cm long, making an acute angle with AB (i)
other than 90° (see adjoining figure (ii)).
Now we need to identify only one more point (say C) to D D 5 cm C
make this a four-sided figure. This point C should be 5 cm
away from both B and D. We have already learnt this in 5 cm 5 cm 5 cm
construction 11.
Step 3: Set a distance of 5 cm between the legs of a compass. A 5 cm B A 5 cm B
First put the pointer at B, make a small arc, then put the (ii) (iii)
pointer at D, and make a small arc to cut the previous arc at C. Join points C to B and C to D. ABCD
is the required 4-sided figure having all sides equal to 5 cm, but it is not a square (see figure (iii)).
Exercise 8.4

1. By making a good estimate of the measures according to your wisdom, construct a rectangle. Divide
the rectangle into two squares with two holes at the centre of the squares.
2. Construct a 4-sided figure in which all sides are equal to 6 cm, but it is not a square.
3. Construct a square with a side length of 6 cm with circular arcs of radius 6 cm on the inner side of
its boundary.
4. Construct the given figure. Square of (NCERT)
(Hint: See construction 21) side 3 cm

Square of
side 5 cm

Square of
side 7 cm

238 Mathematics-6