Page 234 - Ganit Kaushal

8.8 THE ARTWORK

Now, based on the knowledge gained so far, let us construct the following artwork.

1. The House

Construction 12: Construct the figure of the given house by a ruler and compass, where all A
the lines forming the border of the house are of length 5 cm. (NCERT)
Sol. The first task is to identify in what sequence the lines and curves have to be drawn. 5 cm 5 cm
This picture of the house can be visualised in two parts — the lower half and the
upper half. The upper half, ABC, contains a triangle and a curve and the lower half, B C
BDEC, contains only straight lines. So, the lower half can be easily constructed. 5 cm 1 cm 5 cm
Let us construct the lower part first. Follow the steps given below:
Step 1: Draw a line DE, 5 cm long, with the help of a ruler and pencil. Now using D 2 cm E
a protractor, draw perpendiculars to the line DE at points D and E, both 5 cm long. 5 cm
Mark the end points of these perpendiculars as B and C, respectively (see adjoining figure (i)).
Step 2: Now, take a distance of 2 cm between the legs of a compass (see figure (ii)).

Without changing the setting of the compass,
put the pointer at D and draw an arc cutting B C B C
the line DE. Likewise, put the pointer on
E and draw an arc cutting ED. We get two
points of intersection of the two arcs on line
DE (see figure (iii)). D E D E
Step 3: At these two points of intersection (i) (ii) (iii)
obtained in step 2, draw a rectangle of sides (2 cm × 1 cm). (as explained in construction 6) (see
adjoining figure (iv)).
Now, locate a point A that is at a distance of 5 cm from the points B and C. This can be done using the
steps in construction 11.
Step 4: Fix a distance of 5 cm between the legs of a compass. Without changing the settings of the
compass, put the pointer at B and draw A A
an arc. Now, put the pointer at point C
and draw an arc to cut the previous arc at
point A. Join AB and AC (see figure (v)).
Step 5: With the settings of the compass B C B C B C
still the same, put the pointer at A and
draw an arc joining B and C. After
rubbing out all the supporting arcs used
during the construction, we get the final D E D E D E
picture of our house (see figure (vi)). (iv) (v) (vi)
After completing the construction, readers are advised to measure all the distances AB, AC, BD, DE, EC and
the sides of the entrance of the house.
Are they all exactly the same as required?
Yes, they are. Great! Enjoy your house.

232 Mathematics-6