NCERT Solutions for Class 6 Maths Chapter 8 - Playing with Constructions Exercise 8.3

Exercise 8.3

1. Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties. 

Ans: 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.

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

Ans:We shall draw a rectangle of the form shown in Fig. 1.

Step 1. Using a ruler, draw a line AB equal to 10 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 at A such that AP = 2 cm. Using a ruler, mark point Q on the perpendicular at B such that BQ = 2 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 10 cm.
Using a protractor, verify that ∠P and ∠Q are 90° each.

Step 6. We have:
(i) AB = PQ = 10 cm and AP = BQ = 2 cm
(ii) ∠A = ∠B = ∠P = ∠Q = 90°.

Step 7. ABQP in Fig. 5 is the required rectangle of sides 2 cm and 10 cm.

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

• all the angles are equal to 90º but 

• opposite sides are not equal?

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

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

Step 3. Using a ruler, mark point P on the perpendicular at A such that AP = 4 cm.
Using a ruler, mark point Q on the perpendicular at B such that BQ = 2 cm, which is not equal to AP. (Fig. 3).

Step 4. In Fig. 3, the opposite sides of AP and BQ are not equal. Join P and Q using a ruler. Erase the lines above P and Q (Fig. 4).

Step 5. Using a protractor, we find that neither ∠P nor ∠Q is 90°.

Step 6. We conclude that it is not possible to construct a 4-sided figure in which all angles are 90° and opposite sides are not equal.

Benefits of NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.3 Playing with Constructions

• The solutions offer clear, step-by-step explanations for constructing various geometric shapes, aiding in a thorough comprehension of the concepts.

• Diagrams and illustrations are included to help students visualize the construction processes, reinforcing their spatial awareness.

• The exercise includes a variety of problems, allowing students to practice and solidify their skills in geometric constructions.

• The solutions are directly aligned with the NCERT syllabus, ensuring that students are studying relevant content for their exams.

• Engaging with these solutions encourages students to think critically and develop problem-solving skills through practical applications.

• Available for free in PDF format, these solutions can be easily downloaded and accessed at any time, making studying more flexible.

• By mastering the construction of shapes, students gain confidence in their mathematical abilities, preparing them for more complex topics in the future.

Class 6 Maths Chapter 8: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 8 - Playing with Constructions

Conclusion

NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.3, "Playing with Constructions," offer significant benefits for students. These solutions not only simplify the process of constructing various geometric shapes but also enhance understanding and boost confidence in mathematical skills. With clear explanations, visual aids, and ample practice opportunities, students are well-equipped for effective exam preparation. The solutions foster critical thinking and support independent learning, making mathematics engaging and accessible. By utilizing these resources, students can build a solid foundation in geometry, paving the way for success in future mathematical challenges. Explore the NCERT Solutions today to enhance your learning experience!

Chapter-wise NCERT Solutions Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Class 6  Maths 

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.