Playing with Constructions Class 6 Solutions Question Answer

By using Ganita Prakash Book Class 6 Solutions and Chapter 8 Playing with Constructions Class 6 NCERT Solutions Question Answer, students can improve their problem-solving skills.

Class 6 Maths Chapter 8 Playing with Constructions Solutions

Playing with Constructions Class 6 Solutions Questions and Answers

8.1 Artwork Construct (Page No. 190 – 191)

Question 1.
What radius should be taken in the compass to get this half circle? What should be the length of AX?
Solution:
The diameter AX of the half circle shown in the figure is half length of line segment AB. So, AX = \(\frac{8}{2}\) = 4 cm.
To draw this half circle, we should take radius half of AX, i.e., 2 cm in the compass.

Question 2.
Take a central line of a different length and try to draw the wave on it.
Solution:
Try it yourself

Question 3.
Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure ‘A Person’).
The challenge here’is to get both the waves to be identical. This may be tricky!
Solution:
To make waves smaller than the half circle, you should set the compass to a radius smaller than the one used for the circle waves.

8.2 Squares and Rectangles Figure it Out (Page 194)

Question 1.
Draw a configuration of one rectangle and four squares on a square dot paper as shown in the given figure.

What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.
Solution:
Step 1. Take a square dot paper and mark a dot on it at A. Start from A move 10 dots to the right and mark the tenth dot at B.
Step 2. Start from B and move 6 dots above B and mark the 6th dot as C. Start from A and move 6 dots above A and mark the 6th dot as D. Join AB, BC, CD, and DA.
Step 3. Take points E, F, G, and H on the dot paper as shown in the figure.
Step 4. Take points I, J, K, and L at a distance of 4 dots from E, F, G, and H respectively. Join IE, FJ, GK, and LH.
Step 5. On LH and GK, construct squares above the rectangle.
Step 6. On IE and FJ, construct squares below the rectangle.

Step 7. The figure is the required configuration of one rectangle and four squares on a square dot paper.

Question 2.
Identify if there are any squares in this collection. Use measurements if needed.

Think: Is it possible to reason out if the sides are equal or not, and if the angles are right or not without using any measuring instruments in the above figure? Can we do this by only looking at the position of comers in the dot grid?
Solution:
In figure A, all sides are 4 units in the dot grid and all angles are 90°. So, figure A represents a square in the dot grid.

Question 3.
Draw at least 3 rotated squares and rectangles on a dot grid. Draw them such that their corners are on the dots. Verify if the squares and rectangles that you have drawn satisfy their respective properties.
Solution:

8.3 Constructing Squares and Rectangles Construct (Page No. 197)

Question 1.
Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.
Solution:
We shall draw a rectangle of the form shown in Fig. 1.

Step 1. Using a ruler, draw a line AB equal to 6 cm. (Fig. 2)

Step 2. Using a protractor, draw perpendicular lines at A and B (Fig. 3)

Step 3. Using a ruler, mark point P on the perpendicular line at A such that AP = 4 cm. Using a ruler, mark point Q on the perpendicular line at B such that BQ = 4 cm. (Fig. 4).

Step 4. Join P and Q using a ruler. Erase the lines above P and Q. (Fig. 5).

Step 5. Using a ruler, verify that PQ is of length 6 cm.
Using a protractor, verify that ∠P and ∠Q are 90° each.
Step 6. We have:
(i) AB = PQ = 6 cm and AP = BQ = 4 cm
(ii) ∠A = ∠B = ∠Q = ∠P = 90°.
Step 7. ABQP in Fig. 5 is the required rectangle of sides 4 cm and 6 cm.

Question 2.
Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both the rectangle properties.
Solution:
Do it yourself.

Question 3.
Is it possible to construct a 4-sided figure in which—

• all the angles are equal to 90° but
• opposite sides are not equal?

Solution:
Let us draw a line segment PQ of any length.

Now, mark a point to draw a perpendicular to PQ through P. and mark point S on the perpendicular at any length using ruler.

Again repeat the previous step at points Q and S, to get the perpendiculars on PQ and PS respectively. Let the perpendiculars drawn intersect at point R.

Now, measure ∠R, which is 90°.
So, ∠P = ∠Q = ∠R = ∠S = 90°
Also, measure PQ, QR, RS and PS.

Here, PQ = SR and PS = QR
∴ It is not possible to construct a 4-sided figure with the given conditions.

8.5 Exploring Diagonals of Rectangles and Squares Construct (Page No. 211)

Question 1.
Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.
Solution:
Let’s start with a rough diagram
Step 1: AB is any length or arbitrary length.


Step 2:

Step 3:
Draw a perpendicular to line AB at the point A.

Now ∠A is divided into two angles. One measures 50°. The other angle is 40°.
Step 4:

Draw a line perpendicular to BC at C to get the point D.

Question 2.
Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?
Solution:
Do yourself.

Question 3.

Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
Solution:
First draw the base AB of length 4 cm.

Now, draw a perpendicular to line AB at point B. Let us call this line m.

Now, using a ruler, take the distance of 8 cm in a compass, and from A, mark an arc cutting line m at C. Join AC.

Now, construct perpendiculars to AB and BC at points A and C respectively. The point where these perpendiculars intersect is the fourth point D.

Thus, ABCD is a rectangle with side AB = 4 cm and diagonal AC = 8 cm.

Question 4.
Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.
Solution:
Steps
(i) Draw a line segment AB = 3 cm.

(ii) At B, draw a perpendicular line BY.

(iii) Take an arc of length 7 cm on a compass and draw the arc to cut the perpendicular BY at the point C.

(iv) At the points C and A draw two perpendiculars which will intersects at the point D.

Here, ABCD is the required rectangle.

8.6 Points Equidistant from Two Given Points Construct (Page No. 215)

Question 1.
Construct a bigger house in which all the sides are of length 7 cm.
Solution:
Draw a rough diagram

Step 1: Draw a line DE is 7 cm.

Step 2: Draw DB And EC is 7 cm on the line DE at the points D and E respectively.

Step 3:

We need to locate point A which is a of distance 7 cm from points B and C. You might have realized that this can be done using a ruler.
Step 4: We measure the 7 cm in compass and draw an arc at B and C.

Join A to B and A to C in straight lines.
Step 5: Take 7 cm radius in the compass and from A, draw the arc touching B and C as shown in the figure.

Question 2.
Try to recreate A Person’, ‘Wavy Wave’ and ‘Eyes’ from the section. Artwork, using ideas involved in the ‘House’ construction.
Solution:
Do it by yourself

Question 3.
Is there a 4-sided figure in which all the sides are equal in length but are not squares? If such a figure exists, can you construct it?
Solution:
Step 1. Draw a line and take points A and B on it such that AB = 5 cm, say. (Fig. 1)

Step 2. Using a protractor, take points C and D such that angles on the right of A and on the right of B are 60° each. (Fig. 2)

Step 3. Using a ruler, take point P on AC such that AC = 5 cm and Q on BD such that BD = 5 cm. Join P and Q. (Fig. 3)

Step 4. Using a ruler, we measure the distance PQ. PQ is equal to 5 cm. Thus, in Figure ABQP, each side is equal to 5 cm. Here ∠A is 60°, which is not equal to 90°.
∴ ABQP is not a square.
Step 5. We find that there are 4-sided figures in which all the sides are equal in length but are not squares.