NCERT Solutions for Class 6 Maths Chapter 8 Playing with Constructions

Class 6 Playing with Constructions Question Answer

The Playing with Constructions Class 6 questions and answers focus on using a ruler and compass to construct figures and understand their properties.

What is the radius of a circle?

The radius is the distance from the centre of a circle to any point on its circumference.

What properties does a rectangle have?

A rectangle has equal opposite sides, and all four angles are 90°.

What properties does a square have?

A square has four equal sides and four right angles.

Can a square remain a square after rotation?

Yes. Rotation does not change the lengths of its sides or the measures of its angles.

Why is a rough figure useful before construction?

A rough figure helps identify the required measurements, points, lines, and sequence of construction steps.

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Playing with Constructions Class 6 Worksheet with Answers

Fill in the blanks

1. The distance from the centre of a circle to any point on it is called the radius.

2. A rectangle has all its angles equal to 90°.

3. A square has four equal sides.

4. A compass can be used to draw a circle.

5. The line joining two opposite corners of a rectangle is called a diagonal.

True or False

1. All four sides of a rectangle are always equal. — False

2. All angles of a square are 90°. — True

3. A compass can be used to draw a circle. — True

4. Rotating a square changes its side lengths. — False

5. Opposite sides of a rectangle are equal. — True

Read More - NCERT Solutions for Class 6 Maths Chapter 3 Number Play

Answer in One Line

1. What is a compass used for?
A compass is used to draw circles and arcs and transfer equal lengths.

2. What is a diagonal?
A diagonal joins two opposite vertices of a polygon.

3. What is the radius of a circle?
It is the distance between the centre and any point on the circle.

4. How many right angles does a rectangle have?
A rectangle has four right angles.

5. How many equal sides does a square have?
A square has four equal sides.

Playing with Constructions Class 6 Extra Questions

1. How can you construct a circle with a given radius?

Set the compass to the required radius using a ruler. Keep the pointed end fixed at the centre and rotate the pencil end around it.

2. How do you construct a square with a side of 6 cm?

Draw a 6 cm line segment, construct perpendiculars at its endpoints, mark 6 cm on both perpendiculars, and join the new points.

3. How do you construct a rectangle with sides 4 cm and 6 cm?

Draw a 6 cm line segment, construct perpendiculars at both ends, mark 4 cm on them, and join the marked points.

4. How can you construct a point equidistant from two given points?

Draw arcs of the same radius from both given points. Their intersection gives a point equidistant from the two points.

5. What happens when a square is rotated?

It remains a square because its four sides remain equal and its four angles remain 90°.

Read More: Addition and Subtraction of Time

Class 6 Playing with Constructions: Important Concepts

Circles and Compass

A compass helps construct circles and arcs. When the compass has a fixed radius, every point on the circle is at the same distance from its centre.

Squares and Rectangles

A square has four equal sides and four right angles. A rectangle has equal opposite sides and four right angles.

Constructing Squares and Rectangles

The chapter shows how to construct squares and rectangles when their side lengths are known. A compass can also help transfer lengths accurately during construction.

Exploring Rectangles

Students explore the positions of points on opposite sides of a rectangle and compare the distances between them. The chapter also includes constructions involving rectangles divided into identical squares.

Diagonals of Rectangles and Squares

The diagonals of a rectangle can be compared by construction and measurement. The chapter also explores how diagonals divide angles and what happens in the special case of a square.

Points Equidistant from Two Given Points

To locate a point at the same distance from two given points, equal-radius arcs can be drawn from both points. Their intersection gives the required point.

Class 6 Maths Chapter 8 Construction Questions

The chapter includes construction-based tasks such as:

• Drawing artwork using a ruler and compass

• Constructing squares and rectangles

• Dividing rectangles into identical squares

• Constructing a square inside a rectangle

• Drawing patterns using arcs

• Exploring diagonals of rectangles and squares

• Constructing rectangles using a side and a diagonal

• Finding points equidistant from two given points

• Recreating figures such as a house, eyes, and wavy patterns

These activities help students understand why particular construction steps work instead of simply copying a finished figure. The current NCERT Class 6 Ganita Prakash lists Playing with Constructions as Chapter 8, with sections on artwork, squares and rectangles, constructing squares and rectangles, exploring rectangles, diagonals, and points equidistant from two given points.

Read More: CBSE Class 8 Maths Formulas

Common Mistakes in Geometric Constructions

• Do not change the compass opening while transferring a required length.

• Keep the compass point fixed when drawing a circle or arc.

• Use a sharp pencil for accurate constructions.

• Check measurements before joining points.

• Follow the construction steps in the correct order.

• Do not assume a rotated figure has changed its shape or properties.

Quick Revision: Playing with Constructions

• Compass: Used to draw circles and arcs and transfer lengths.

• Radius: Distance from the centre of a circle to its circumference.

• Square: Four equal sides and four 90° angles.

• Rectangle: Opposite sides equal and four 90° angles.

• Diagonal: Line segment joining opposite vertices.

• Equidistant point: A point having equal distances from two given points.

• Construction: A geometric figure made accurately using instruments such as a ruler and compass.