---
title: "NCERT Solutions Class 6 Maths Ch 8 Playing with Constructions"
url: https://www.swavid.com/maths/class/6/chapter/playing-with-constructions/ncert-solutions
dateModified: 2026-10-07T14:52:17+00:00
---

# NCERT Solutions Class 6 Maths Ch 8 Playing with Constructions

This chapter's questions cover the practical geometric construction of curves, circles, squares, rectangles, and complex shapes using a ruler and compass.

Free PDF (11 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-6/swavid-ncert-solutions-class-6-maths-chapter-8-playing-with-constructions-0b51f7b7d0.pdf

## 8.1 Artwork

### Question 1

*Activity*

Observe the following figures and try drawing them freehand.

**Solution**

1. Observe the given figures consisting of circles, intersecting lines, and shapes in the figure in the textbook (Fig. 8.1).
2. Try drawing these shapes freehand without using any measuring or drawing instruments to practice hand-eye coordination and shape recognition.

**Answer:** Freehand sketches of the given artwork figures.

## Figure it Out

### Question 1

*3 marks · Short answer*

What radius should be taken in the compass to get this half circle? What should be the length of AX?

**Solution**

1. The diameter of the half circle is equal to the length of AX.
2. From the figure in the textbook (Fig. 8.2 or page 191), the length of the central segment AX is half of the total length AB (8 cm).
3. Therefore, the length of AX is $4 \text{ cm}$ and the radius taken in the compass is half of AX, which is $2 \text{ cm}$.

**Answer:** Radius = 2 cm, length of AX = 4 cm

> Common mistake: Confusing the radius of the half circle with the length of AX.

### Question 2

*Activity*

Take a central line of a different length and try to draw the wave on it.

**Solution**

1. Take a straight line of any desired length, such as $6\text{ cm}$ or $10\text{ cm}$, using a ruler.
2. Mark the midpoints and use a compass with an appropriate fixed radius to draw alternating upper and lower semicircular arcs.
3. Observe how changing the length of the central line affects the number and size of the waves.

**Answer:** Activity completed by drawing waves on a new central line.

### Question 3

*Activity*

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**

1. Fix a radius in the compass that is smaller than half the segment length so that the arc forms less than a semicircle.
2. Keep the compass radius and center positions consistent for each section to ensure the waves are identical.
3. Draw alternating arcs above and below the central line to form the smaller wave pattern.

**Answer:** Activity completed by recreating identical smaller waves.

## Which of the following is not a name for this square?

### Question 1

*1 mark · MCQ*

Which of the following is not a name for this square?

- PQSR
- SPQR
- RSPQ
- QRSP

**Solution**

1. In a valid name, the corners must occur in an order of travel around the square, starting from any corner.
2. The given square has corners S, P, R, and Q in clockwise or counter-clockwise order, but PQSR goes diagonally across instead of around the boundary.

**Answer:** (1) PQSR

> Common mistake: Naming the shape by jumping across opposite corners instead of following the perimeter.

## Figure it Out

### Question 1

*Activity*

Draw the rectangle and four squares configuration (shown in Fig. 8.3) on a dot paper. What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.

**Solution**

1. Draw a rectangle on the dot paper.
2. Leave one dot distance diagonally from each corner of the rectangle.
3. Place the four smaller squares symmetrically at the four corners.

**Answer:** The four squares are placed symmetrically by leaving a consistent dot distance diagonally from the rectangle corners.

### Question 2

*3 marks · Short answer*

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

**Solution**

1. Observe the shapes A, B, C, and D in the collection on the dot grid.
2. Measure the sides and check the grid positions for right angles.
3. Identify that shape A satisfies all properties of a square with equal sides and right angles.

**Answer:** Shape A is a square.

> Common mistake: Confusing a rotated square with a rhombus by misjudging the internal angles.

### Question 3

*Activity*

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**

1. Select grid dots to form closed 4-sided figures at various angles.
2. Ensure all interior angles are $90^\circ$ by following the grid alignment for rectangles and squares.
3. Verify that squares have all equal sides and rectangles have opposite equal sides.

**Answer:** Rotated squares and rectangles are successfully drawn with their corners on the dots and verified.

## Construct

### Question 1

*3 marks · Short answer*

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

**Solution**

1. Draw a line segment AB of length 4 cm.
2. Construct perpendiculars at A and B using a protractor or compass, and cut off AD = 6 cm and BC = 6 cm.
3. Join CD to complete the rectangle ABCD.
4. Measure the angles and sides to verify that $\angle A = \angle B = \angle C = \angle D = 90^\circ$ and opposite sides $AB = CD = 4\text{ cm}$ and $AD = BC = 6\text{ cm}$.

**Answer:** $\angle A = \angle B = \angle C = \angle D = 90^\circ$ and $AB = CD = 4\text{ cm}, AD = BC = 6\text{ cm}$.

> Common mistake: Not drawing accurate $90^\circ$ angles at the corners.

### Question 2

*3 marks · Short answer*

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

**Solution**

1. Draw a line segment PQ of length 10 cm.
2. Construct perpendiculars at P and Q, and mark PS = 2 cm and QR = 2 cm.
3. Join SR to complete the rectangle PQRS.
4. Check that all angles are $90^\circ$ and opposite sides are equal, with $PQ = SR = 10\text{ cm}$ and $PS = QR = 2\text{ cm}$.

**Answer:** $\angle P = \angle Q = \angle R = \angle S = 90^\circ$ and $PQ = SR = 10\text{ cm}, PS = QR = 2\text{ cm}$.

> Common mistake: Confusing the length and breadth while marking the perpendicular sides.

### Question 3

*3 marks · Short answer*

Is it possible to construct a 4-sided figure in which—
• all the angles are equal to 90º but
• opposite sides are not equal?

**Solution**

1. Recall the properties of a rectangle where all interior angles are equal to $90^\circ$.
2. In any 4-sided figure with all four angles equal to $90^\circ$, the opposite sides must be parallel and equal in length.
3. Therefore, it is not possible to have a 4-sided figure with all angles equal to $90^\circ$ where opposite sides are not equal.

**Answer:** No, it is not possible.

> Common mistake: Assuming a quadrilateral can have four right angles without opposite sides being equal.

## Construct

### Question 1

*3 marks · Short answer*

Construct a rectangle that can be divided into 3 identical squares as shown in the figure.

**Solution**

1. Draw a line segment of any convenient length for the base of the rectangle.
2. Construct perpendiculars at the endpoints and use a compass to mark equal segments corresponding to the side lengths of the three identical squares.
3. Join the points to complete the rectangle that is divided into 3 identical squares.

**Answer:** A rectangle whose length is three times its breadth, divided into 3 identical squares.

> Common mistake: Taking the length equal to the breadth instead of making the length three times the breadth for three squares.

## Construct

### Question 1

*3 marks · Short answer*

A Square within a Rectangle: Construct a rectangle of sides 8 cm and 4 cm. How will you construct a square inside, as shown in the figure, such that the centre of the square is the same as the centre of the rectangle?

**Solution**

1. Draw a rectangle ABCD of length $8\text{ cm}$ and breadth $4\text{ cm}$.
2. Draw the two diagonals of the rectangle to find their intersection point, which is the centre of the rectangle.
3. Construct a square inside the rectangle such that its centre coincides with the intersection point and its sides are parallel to the rectangle's sides.

**Answer:** A square constructed inside the $8\text{ cm} \times 4\text{ cm}$ rectangle sharing the same centre.

> Common mistake: Placing the inner square off-centre by not locating the geometric centre of the rectangle first.

### Question 2

*3 marks · Short answer*

Falling Squares: Construct the falling squares figure as shown, ensuring the squares of side 7 cm, 5 cm, and 3 cm are aligned correctly.

**Solution**

1. Draw a square of side $7\text{ cm}$ using a ruler and set square or protractor for $90^\circ$ angles.
2. Position the next square of side $5\text{ cm}$ such that its top-left corner touches the bottom-right corner of the $7\text{ cm}$ square along a diagonal alignment.
3. Construct the third square of side $3\text{ cm}$ aligned similarly at the corner of the $5\text{ cm}$ square.

**Answer:** Falling squares of sides $7\text{ cm}$, $5\text{ cm}$, and $3\text{ cm}$ aligned diagonally.

> Common mistake: Misaligning the squares so that their corners do not touch properly along the diagonal path.

### Question 3

*Activity*

Shadings: Construct this. Choose measurements of your choice. Note that the larger 4-sided figure is a square and so are the smaller ones.

**Solution**

1. Draw a large outer square of chosen dimensions using a ruler and set square.
2. Divide the large square into smaller identical squares using parallel lines.
3. Shade alternate smaller squares with hatched pattern lines as shown in the figure.

**Answer:** A large square divided into smaller squares with alternate shading.

### Question 4

*3 marks · Short answer*

Square with a Hole: Construct a square with a circular hole centred at the same point as the centre of the square.

**Solution**

1. Construct a square of desired side length.
2. Draw the two diagonals of the square to find their intersection point as the centre.
3. Place the compass tip at this centre and draw a circle of appropriate radius to form the circular hole.

**Answer:** A square with a concentric circular hole at its centre.

> Common mistake: Drawing the circle off-centre by guessing instead of using the intersection of diagonals.

### Question 5

*3 marks · Short answer*

Square with more Holes: Construct a square divided into four quadrants, each with a circular hole.

**Solution**

1. Construct a large square and draw its horizontal and vertical lines of symmetry dividing it into four equal smaller squares.
2. Find the centre of each of the four smaller squares by drawing their diagonals.
3. Draw a circle using a compass centred at the middle of each quadrant.

**Answer:** A square divided into four quadrants, each containing a circular hole.

> Common mistake: Placing the circles without dividing the main square into symmetric quadrants first.

### Question 6

*3 marks · Short answer*

Square with Curves: Construct a square with 8 cm sidelengths where the four sides bulge uniformly inward as arcs.

**Solution**

1. Construct a square with $8\text{ cm}$ sidelengths using a ruler and set square.
2. Determine the appropriate compass placement points outside or inside the square corresponding to each side.
3. Draw uniform inward-bulging arcs on all four sides to form the curved square figure.

**Answer:** A square with $8\text{ cm}$ sidelengths and uniformly curved inward sides.

> Common mistake: Freehand sketching the curves instead of using a compass with properly placed centres for uniform arcs.

## Construct

### Question 1

*3 marks · Short answer*

Construct a rectangle in which one of the diagonals divides the opposite angles into 60° and 30°.

**Solution**

1. Draw a line segment AB of any convenient arbitrary length.
2. Draw a line making an angle of $60^\circ$ at point A and draw a perpendicular to AB at point B to intersect it at point C.
3. Draw a perpendicular to line BC at point C to locate point D such that AD is equal and parallel to BC.
4. Join CD to complete the required rectangle ABCD where the diagonal divides the opposite angles into $60^\circ$ and $30^\circ$.

**Answer:** Rectangle ABCD constructed using a side and angles.

> Common mistake: Confusing the $60^\circ$ and $30^\circ$ angles with the adjacent sides or misplacing the perpendicular lines.

## Construct

### Question 1

*3 marks · Short answer*

Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.

**Solution**

1. Draw a line segment AB of an arbitrary length as the base.
2. Draw a line perpendicular to AB at point B.
3. Draw a ray from A making an angle of $50^\circ$ with AB to intersect the perpendicular at C.
4. Draw a perpendicular to BC at C and mark point D such that AD = BC, then join CD to get the required rectangle ABCD.

**Answer:** Rectangle ABCD constructed where the diagonal AC divides angle A into $50^\circ$ and angle C into $40^\circ$.

> Common mistake: Measuring the wrong angle or confusing the adjacent side lengths.

### Question 2

*3 marks · Short answer*

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**

1. Draw a line segment AB of an arbitrary length as the base.
2. Draw a perpendicular to AB at point B.
3. Draw a ray from A making an angle of $45^\circ$ with AB to intersect the perpendicular at C.
4. Complete the rectangle ABCD by constructing perpendiculars, and observe that all four sides become equal, making the rectangle a square.

**Answer:** Rectangle ABCD constructed where the diagonal divides the opposite angles into $45^\circ$ and $45^\circ$, and the sides of the rectangle are all equal.

> Common mistake: Not recognizing that equal opposite angles formed by the diagonal make the rectangle a square.

### Question 3

*3 marks · Short answer*

Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.

**Solution**

1. Draw the base side PQ measuring $4\text{ cm}$.
2. Draw a line perpendicular to PQ passing through Q.
3. Take a radius of $8\text{ cm}$ in the compass with centre P, and draw an arc to intersect the perpendicular line at S.
4. Complete the rectangle PQRS by drawing perpendiculars from P and S of length equal to QR.

**Answer:** Rectangle PQRS with side $4\text{ cm}$ and diagonal $8\text{ cm}$ constructed successfully.

> Common mistake: Taking the diagonal length from the wrong vertex or incorrect compass radius.

### Question 4

*3 marks · Short answer*

Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.

**Solution**

1. Draw the base side AB measuring $3\text{ cm}$.
2. Draw a line perpendicular to AB passing through B, let it be line l.
3. Take a radius of $7\text{ cm}$ in the compass with centre A, and draw an arc intersecting line l at D.
4. Complete the rectangle ABCD by constructing perpendiculars to find the fourth point C.

**Answer:** Rectangle ABCD with side $3\text{ cm}$ and diagonal $7\text{ cm}$ constructed successfully.

> Common mistake: Drawing the perpendicular at the wrong end or measuring the diagonal from the incorrect corner.

## Construct

### Question 1

*3 marks · Short answer*

House: Recreate this figure. Note that all the lines forming the border of the house are of length 5 cm.

**Solution**

1. Draw the baseline DE of length 5 cm using a ruler.
2. Draw perpendicular lines of height 2 cm at the ends to form the door and walls of height 5 cm.
3. Construct point A at a distance of 5 cm from both B and C using a compass with a 5 cm radius.
4. Join AB and AC with straight lines, and draw the arc from B to C using a radius of 5 cm centred at A.

**Answer:** A house constructed with all border lines and roof arcs of length 5 cm.

> Common mistake: Using a ruler with trial and error for point A instead of using arcs drawn with a compass.

## Construct

### Question 1

*3 marks · Short answer*

Construct a bigger house in which all the sides are of length 7 cm.

**Solution**

1. Draw the base DE of length $7\text{ cm}$ using a ruler.
2. Draw perpendiculars of length $7\text{ cm}$ at points D and E to get points B and C, and construct the central door of width $2\text{ cm}$ and height $3\text{ cm}$ on DE.
3. Take a radius of $7\text{ cm}$ in the compass and with B and C as centres, draw arcs intersecting at point A, then join A to B and A to C, and draw the inner arc.

**Answer:** A bigger house with all outer sides of length $7\text{ cm}$ is constructed.

> Common mistake: Taking incorrect radius for the roof arcs or placing the compass at the wrong centre.

### Question 2

*3 marks · Short answer*

Try to recreate 'A Person', 'Wavy Wave', and 'Eyes' from the section 'Artwork', using ideas involved in the 'House' construction.

**Solution**

1. Use a compass with a fixed radius to draw circles and arcs for 'A Person', 'Wavy Wave', and 'Eyes'.
2. Ensure that supporting curves and symmetrical arcs are constructed using intersecting arcs similar to the 'House' method.
3. Refine the figures so that the curves are smooth, identical, and properly aligned.

**Answer:** Figures 'A Person', 'Wavy Wave', and 'Eyes' are recreated using compass and ruler constructions.

> Common mistake: Failing to maintain the same radius across symmetrical parts of the drawings.

### Question 3

*3 marks · Short answer*

Is there a 4-sided figure in which all the sides are equal in length but is not a square? If such a figure exists, can you construct it?

**Solution**

1. State that such a 4-sided figure exists and it is called a rhombus.
2. Draw a line segment of a given length and use a compass opened to the same side length to draw intersecting arcs from the endpoints.
3. Connect the intersection points to form a rhombus where all sides are equal in length but interior angles are not $90^\circ$.

**Answer:** Yes, a rhombus is a 4-sided figure with all equal sides that is not a square, and it can be constructed using a compass and ruler.

> Common mistake: Drawing angles of $90^\circ$ at the corners, which would make the figure a square instead of a rhombus.

## Frequently asked questions

### How many total questions are there in NCERT Solutions for Class 6 Maths Chapter 8 Playing with Constructions?

This chapter is based on the new NCERT book for the 2026-27 session and contains a total of 28 questions distributed across various sections. You can find step-by-step solutions for all these questions in the free PDF available on this page.

### Which topics do the questions cover in Class 6 Maths Chapter 8 Playing with Constructions?

The questions cover concepts such as freehand drawing of geometrical artwork, constructing wave arcs, naming conventions for squares and rectangles, and drawing rotated shapes on a dot grid. Other topics include properties of quadrilaterals, constructing rectangles with given dimensions or diagonals, and compass construction of rhombuses and geometric artwork.

### Which type of questions are considered challenging in this chapter and how should we approach them?

Questions involving the construction of rectangles using a side and diagonal angles or compass constructions of complex artwork are generally the most detailed. To approach them, carefully read the given dimensions, use a ruler and compass accurately, and follow the step-by-step solutions provided in SwaVid's free PDF on this page.

### How can I write answers for full marks in Class 6 Maths Chapter 8?

To secure full marks, you should write down every step of construction clearly and maintain neatness in your geometric drawings. Referring to the detailed solutions on this page will help you understand the proper format and method to present your answers.

### Is the free PDF for Class 6 Maths Chapter 8 Playing with Constructions available?

Yes, the complete free PDF containing structured solutions for all the questions in the new NCERT book for the 2026-27 session is available right here on this SwaVid page.

## Related pages

- [Class 6 Maths chapters](https://www.swavid.com/maths/class/6)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student