Class 6 Maths Chapter 8 Solutions: Playing with Constructions

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Solution sheet 1

Section 8.1 · Figure it out

NCERT Class 6 Maths Chapter 8, question 1 — Source question

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

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2 cm. AX = 4 cm.

Source worked solution for Class 6 Chapter 8, question 1, part 1 — Source worked answer · part 1

Section 8.1 · Figure it out

NCERT Class 6 Maths Chapter 8, question 2 — Source question

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

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Source worked solution for Class 6 Chapter 8, question 2, part 1 — Source worked answer · part 1

Section 8.1 · Figure it out

NCERT Class 6 Maths Chapter 8, question 3 — Source 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!

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Page no. 193 Section 8.2

Source worked solution for Class 6 Chapter 8, question 3, part 1 — Source worked answer · part 1

Page no. 193 · Section 8.2

NCERT Class 6 Maths Chapter 8, question 4 — Source question

Which of the following is not a name for this square? 1. PQSR 2. SPQR [1] 3. RSPQ 4. QRSP

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PQSR is not a name for the given square. Page no. 194 Section 8.2 Figure it out Draw a rectangle & then leave one dot distance diagonally to place the four smaller squares.

Source worked solution for Class 6 Chapter 8, question 4, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 4, part 2 — Source worked answer · part 2

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Solution sheet 2

Section 8.2 · Figure it out

NCERT Class 6 Maths Chapter 8, question 5 — Source question

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

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A is a square. 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 corners in the dot grid? Ans. Yes, In the above figure without measuring one can reason out for equal sides & right angles. Yes, the position of the points on the grid paper makes it possible

Source worked solution for Class 6 Chapter 8, question 5, part 1 — Source worked answer · part 1

Think: Is it possible to reason out if the sides are equal or not, and if the angles are

NCERT Class 6 Maths Chapter 8, question 6 — Source 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.

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[2] Page no. 197 Section 8.3 Construct

Source worked solution for Class 6 Chapter 8, question 6, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 6, part 2 — Source worked answer · part 2

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Solution sheet 3

Section 8.3 · Construct

NCERT Class 6 Maths Chapter 8, question 7 — Source question

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

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A = B = C = D = 90 AB = CD = 4 cm & AD = BC = 6 cm.

Source worked solution for Class 6 Chapter 8, question 7, part 1 — Source worked answer · part 1

Section 8.3 · Construct

NCERT Class 6 Maths Chapter 8, question 8 — Source question

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

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P = Q = R = S = 90 PQ = SR = 10 cm & PS = QR = 2 cm

Source worked solution for Class 6 Chapter 8, question 8, part 1 — Source worked answer · part 1

Source solution page 33

NCERT Class 6 Maths Chapter 8, question 9 — Source question

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?

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No. Page no. 198 Section 8.4

Source worked solution for Class 6 Chapter 8, question 9, part 1 — Source worked answer · part 1

Page no. 198 · Section 8.4

NCERT Class 6 Maths Chapter 8, question 10 — Source question

Is there a shorthand way of writing it down? In all the sentences, only the position of X, Y and the length XY changes. So we could write this as: Distance of X from A Distance of Y from B Length of XY

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Distance of X from A Distance of Y from B Length of XY 5 mm 1 cm 2 cm 3 cm 1 cm 4 cm 7.4 cm 7 cm 7.3 cm [3] Page No. 199

Source worked solution for Class 6 Chapter 8, question 10, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 10, part 2 — Source worked answer · part 2

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Solution sheet 4

Page No. 199

NCERT Class 6 Maths Chapter 8, question 11 — Source question

Have you checked what happens to the length XY when X and Y are placed at the same distance away from A and B, respectively? For example, as in the cases like these: Distance of X from A Distance of Y from B Length of XY 5 mm 1 cm 1 cm 5 mm 5 cm 1 cm 4 cm And so on.

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Distance of X from A Distance of Y from B Length of XY 5 mm 1 cm 1 cm 5 mm 5 mm 1 cm 1 cm 5 mm 7 cm 7 cm 7 cm Page no. 199

Source worked solution for Class 6 Chapter 8, question 11, part 1 — Source worked answer · part 1

Page no. 199

NCERT Class 6 Maths Chapter 8, question 12 — Source question

In each of these cases, observe i. how the length XY compares to that of AB and ii. the shape of the 4-sided figure ABYX.

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i. XY = AB ii. ABYX is a rectangle

Source worked solution for Class 6 Chapter 8, question 12, part 1 — Source worked answer · part 1

Page no. 199

NCERT Class 6 Maths Chapter 8, question 13 — Source question

How does the farthest distance between X and Y compare with the length of AC? BD?

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The farthest distance between X and Y is equal to AC or BD. Construct

Source worked solution for Class 6 Chapter 8, question 13, part 1 — Source worked answer · part 1

Construct

NCERT Class 6 Maths Chapter 8, question 14 — Source question

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

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Hint: Take the length of the rectangle three times its breadth. Page no. 201 Give the lengths of the sides of a rectangle that cannot be divided into — • two identical squares; • three identical squares Ans. • Lengths of sides of a rectangle that cannot be divided into two identical squares: Length = 4 cm and Breadth = 2.5cm (Try for more!) • Length of sides of a rectangle that cannot be divided into three identical squares: Length = 7cm and Breadth = 2cm (Try for other possibilities.) [4] Page no. 201

Source worked solution for Class 6 Chapter 8, question 14, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 14, part 2 — Source worked answer · part 2

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Solution sheet 5

Page no. 201

NCERT Class 6 Maths Chapter 8, question 15 — Source question

4. Square with a Hole

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The centre of the circle should be at the meeting point of two line segments connecting opposite vertices. Page no. 204 Section 8.5 Explore

Source worked solution for Class 6 Chapter 8, question 15, part 1 — Source worked answer · part 1

Page no. 204 · Section 8.5

NCERT Class 6 Maths Chapter 8, question 16 — Source question

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?

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The rectangle should be constructed in such a manner that the two adjacent sides are equal i.e. the rectangle becomes a square. Page no. 211 Construct

Source worked solution for Class 6 Chapter 8, question 16, part 1 — Source worked answer · part 1

Page no. 211 · Construct

NCERT Class 6 Maths Chapter 8, question 17 — Source question

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

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Source worked solution for Class 6 Chapter 8, question 17, part 1 — Source worked answer · part 1

Construct · Q.1. Construct a rectangle in which one of the diagonals divides the opposite angles into

NCERT Class 6 Maths Chapter 8, question 18 — Source 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?

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[5]

Source worked solution for Class 6 Chapter 8, question 18, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 18, part 2 — Source worked answer · part 2

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Solution sheet 6

Q.1. Construct a rectangle in which one of the diagonals divides the opposite angles into · Q.2. Construct a rectangle in which one of the diagonals divides the opposite angles into

NCERT Class 6 Maths Chapter 8, question 19 — Source question

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

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Source worked solution for Class 6 Chapter 8, question 19, part 1 — Source worked answer · part 1

Q.2. Construct a rectangle in which one of the diagonals divides the opposite angles into · Q.3. Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.

NCERT Class 6 Maths Chapter 8, question 20 — Source question

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

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[6] Page no. 215 Construct

Source worked solution for Class 6 Chapter 8, question 20, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 20, part 2 — Source worked answer · part 2

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Solution sheet 7

Page no. 215 · Construct

NCERT Class 6 Maths Chapter 8, question 21 — Source question

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

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[7]

Source worked solution for Class 6 Chapter 8, question 21, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 8, question 21, part 2 — Source worked answer · part 2

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Solution sheet 8

Construct · Q.1. Construct a bigger house in which all the sides are of length 7 cm.

NCERT Class 6 Maths Chapter 8, question 22 — Source question

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

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Source worked solution for Class 6 Chapter 8, question 22, part 1 — Source worked answer · part 1

Q.1. Construct a bigger house in which all the sides are of length 7 cm. · Q.2. Try to recreate ‘A Person’, ‘Wavy Wave’ and ‘Eyes’ from the section Artwork,

NCERT Class 6 Maths Chapter 8, question 23 — Source question

3. 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?

Show solution

[8]

Source worked solution for Class 6 Chapter 8, question 23, part 1 — Source worked answer · part 1

Playing with Constructions Class 6 Solutions

Match, attempt, then check

Solution sheet 1

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

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

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!

Which of the following is not a name for this square? 1. PQSR 2. SPQR [1] 3. RSPQ 4. QRSP

Solution sheet 2

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

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 sheet 3

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

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

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?

Is there a shorthand way of writing it down? In all the sentences, only the position of X, Y and the length XY changes. So we could write this as: Distance of X from A Distance of Y from B Length of XY

Solution sheet 4

Have you checked what happens to the length XY when X and Y are placed at the same distance away from A and B, respectively? For example, as in the cases like these: Distance of X from A Distance of Y from B Length of XY 5 mm 1 cm 1 cm 5 mm 5 cm 1 cm 4 cm And so on.

In each of these cases, observe i. how the length XY compares to that of AB and ii. the shape of the 4-sided figure ABYX.

How does the farthest distance between X and Y compare with the length of AC? BD?

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

Solution sheet 5

4. Square with a Hole

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?

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

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 sheet 6

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

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

Solution sheet 7

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

Solution sheet 8

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

3. 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?