RD Sharma Solutions Class 6 Maths Chapter 13 Quadrilaterals - Free PDF Download

Chapter 13 of RD Sharma Class 6 Maths introduces us to quadrilaterals, which are simple closed figures made of four straight sides and four angles. This chapter helps students understand different types of quadrilaterals like squares, rectangles, parallelograms, rhombuses, and trapeziums based on their sides and angles. We also learn about their basic properties such as opposite sides being equal or angles being right angles. 

Quadrilaterals are not just a part of geometry—they are everywhere in our daily life. From the shape of a notebook, a table, or a window, to tiles on the floor or frames on the wall, quadrilaterals are all around us. This chapter builds a strong foundation in recognizing and understanding these shapes, which helps in practical problem-solving and designing objects in real life.

RD Sharma Solutions Class 6 Maths Chapter 13 Quadrilaterals

As stated in Chapter 13 of RD Sharma Class 6 Maths, quadrilaterals are closed figures with four sides. The chapter deals with the angle sum property of quadrilaterals, different types of sides and angles, and how to identify them in shapes. 

The solutions provided in this chapter help students build a strong foundation in geometry by providing, explanations for all textbook questions in a step-by-step manner. The solutions are made according to the latest syllabus issued by CBSE. It will help you in revision, practice and examination preparation.

Exercises Covered in Chapter 13 – Quadrilaterals

1. Exercise 13.1 – Introduction to Quadrilaterals
2. Exercise 13.2 – Classification of Quadrilaterals
3. Exercise 13.3 – Properties of Quadrilaterals
4. Exercise 13.4 – Angle Sum Property of a Quadrilateral
5. Exercise 13.5 – Solved Examples & Practice Questions

RD Sharma Solutions Class 6 Maths Chapter 13 Quadrilaterals - Extra Questions

1. Define a quadrilateral and explain the sum of its interior angles. Provide a proof for your explanation.

A: A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always
The sum of the interior angles of any quadrilateral is 360°.

Proof:
To prove this, we divide the quadrilateral into two triangles.

Consider a quadrilateral ABCD.

Draw a diagonal AC, which divides the quadrilateral into two triangles: △ABC and △CDA.

We know that:

The sum of interior angles of a triangle = 180°

So, each triangle has angle sum = 180°

Now,

Triangle ABC = 180°

Triangle CDA = 180°

Total = 180° + 180° = 360°

Hence, the sum of all interior angles of a quadrilateral is 360°.

2. Differentiate between a parallelogram and a rhombus. Provide examples of each.

A: A parallelogram is a quadrilateral with opposite sides parallel and equal in length. A rhombus is a special type of parallelogram where all four sides are equal in length. For example, a rectangle is a parallelogram, while a diamond shape is a rhombus.

3. How can you prove that a given quadrilateral is a rectangle using its properties?

A: To prove a quadrilateral is a rectangle, show that it has four right angles. Alternatively, demonstrate that it is a parallelogram with one right angle or that the diagonals are equal in length.

4. Explain the properties of a trapezium and how it differs from other quadrilaterals.

A: A trapezium (or trapezoid) is a quadrilateral with at least one pair of parallel sides. Unlike parallelograms, trapeziums do not have opposite sides equal or parallel. The non-parallel sides are called legs, and the parallel sides are called bases.

5. Calculate the area of a rhombus with diagonals measuring 10 cm and 24 cm.

A: The area of a rhombus can be calculated using the formula:

1/2×10×24=120cm

Q6. What is the significance of the diagonals in a kite, and how do they interact?

A: In a kite, the diagonals intersect at right angles, and one of the diagonals bisects the other. This property is significant in determining the symmetry and area of the kite.

Q7. Describe how to construct a square using only a compass and straightedge.

A: To construct a square:

1. Draw a line segment to be one side of the square.
2. Use a compass to draw arcs from each endpoint, creating intersections that form a perpendicular bisector.
3. Repeat the process to form a right angle.
4. Connect the endpoints to form a square.

Q8. How do you determine if a given quadrilateral is a parallelogram using coordinate geometry?

A: In coordinate geometry, a quadrilateral is a parallelogram if:

Opposite sides are equal in length, or
Opposite sides are parallel (slopes are equal), or
Diagonals bisect each other.

Q9. Prove that the diagonals of a rectangle are equal in length.

A: In a rectangle, opposite sides are equal and parallel. By the Pythagorean theorem, the diagonals, which form right triangles with the sides, are equal because they are the hypotenuses of congruent triangles.

Q10. How can you use the properties of a parallelogram to solve for unknown angles or sides?

A: In a parallelogram, opposite sides are equal, and opposite angles are equal. Adjacent angles are supplementary. These properties can be used to set up equations to solve for unknown angles or sides.

Q11. Describe the process of verifying if a quadrilateral is a kite using its side lengths.

A: A quadrilateral is a kite if it has two distinct pairs of adjacent sides that are equal. This can be verified by measuring the side lengths and checking for the equality of adjacent pairs.
​Q12. How can you determine if a given quadrilateral is a rhombus using its diagonals?

A: A quadrilateral is a rhombus if its diagonals bisect each other at right angles and are not necessarily equal. This can be verified by measuring the diagonals and checking their intersection properties.

Q13. Discuss the role of symmetry in quadrilaterals and provide examples.

A: Symmetry in quadrilaterals refers to the balance and proportion of sides and angles. For example, a square has four lines of symmetry, while a rectangle has two. Symmetry helps in simplifying geometric problems and constructions.

Q14: How do you calculate the area of a trapezium with bases 8 cm and 12 cm, and height 5 cm?

A: The area of a trapezium is calculated using the formula:

1/2 ×(Sum of parallel sides)×Height

In a trapezium, the two parallel sides are often called the bases.

Given:
One base = 8 cm

Other base = 12 cm

Height = 5 cm

Area of a trapezium= 1/1 (8+12)*5= 50 cm^2

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Advantages of using RD Sharma Solutions Class 6 Maths Chapter 13 Quadrilateral

1. Clear Concept Building: The solutions simplify complex ideas related to quadrilaterals, helping students understand shapes like rectangles, squares, parallelograms, and trapeziums with clarity.
2. Step-by-Step Explanations: Every answer is broken down into small, logical steps, making it easier for students to follow the process and learn effective problem-solving methods.
3. Boosts Exam Confidence: Regular practice with these solutions helps students become familiar with question patterns and improves their confidence during school exams.
4. Supports Self-Study: Students can learn independently without always needing a tutor, as the solutions are designed in an easy and student-friendly language.
5. Covers All Textbook Questions: The solutions include answers to all exercise questions in the RD Sharma textbook, ensuring complete preparation and no topic is left out.