CBSE Important Questions Class 6 Maths Chapter 8 – Playing with Constructions

Class 6 Maths Chapter 8 Playing with Constructions is part of the new NCERT textbook Ganita Prakash. It teaches students how to draw accurate figures using only a ruler and a compass. Students learn to draw line segments of a given length, perpendicular lines, circles and arcs, squares and rectangles, and to find a point that is at the same distance from two given points.

These CBSE important questions for Class 6 Maths Chapter 8 cover finding an equidistant point on a map, drawing shapes made of squares, arcs and circles step by step, constructing rectangles from given sides and from a side and a diagonal, rotated squares, dividing a rectangle into equal squares, and spotting the wrong step in a construction. Every question has a clear step-by-step answer in simple English with figures, so students can practise on their own, parents can check the working, and teachers can use them for class tests. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 6 Maths Chapter 8 – Playing with Constructions

Playing with Constructions (New NCERT)
Medium
Q.
Consider the following figure of a “Wavy Wave”.
As the length of the central line is not specified, we can take it to be of any length. Let us take AB to the central line such that the length of AB is 8 cm. Here the first wave is drawn as a half circle.
What radius should be taken in the compass to get this half-circle? What should be the length of AX?
Playing with Constructions (New NCERT)
Medium
Q.
Consider a “Wavy Wave” of the given form.
Take a central line of a different length and try to draw the wave on it.
Playing with Constructions (New NCERT)
Medium
Q.
Try to recreate the figure representing a “Wavy Wave”, where the waves are smaller than a half circle.
Try to recreate the figure where the waves are smaller than a half circle (as appears in the neck of the figure ‘A Person’). The challenge here is to get both the waves to be identical. This may be tricky!
Playing with Constructions (New NCERT)
Medium
Q.
​Draw a configuration of one rectangle and four squares on a square dot paper as shown in the given figure.
​What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.​
Playing with Constructions (New NCERT)
Medium
Q.
Identify if there are any squares in this collection. Use measurements, if needed.
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?
Playing with Constructions (New NCERT)
Medium
Q.
​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.​
Playing with Constructions (New NCERT)
Medium
Q.
​Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.​
Playing with Constructions (New NCERT)
Medium
Q.
Draw a rectangle of sides 2 cm and 10 cm. After drawing check if it satisfies both the rectangle properties.
Playing with Constructions (New NCERT)
Medium
Q.
Is it possible to construct a 4-sided figure in which-
(i) All the angles are equal to 90° but
(ii) Opposite sides are not equal?
Playing with Constructions (New NCERT)
Medium
Q.
Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.
Playing with Constructions (New NCERT)
Medium
Q.
Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?
Playing with Constructions (New NCERT)
Medium
Q.
Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
Playing with Constructions (New NCERT)
Medium
Q.
Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.
Playing with Constructions (New NCERT)
Medium
Q.
Construct a bigger house in which all the sides are of length 7 cm.
Recreate the given figure. Note that all the lines forming the border of the house are of length 7 cm.
Playing with Constructions (New NCERT)
Medium
Q.
Try to recreate ‘A Person’, ‘Wavy Wave’, and ‘Eyes’ from the section Artwork, using ideas involved in the ‘House’ construction.
Playing with Constructions (New NCERT)
Medium
Q.
Is there a 4-sided figure in which all the sides are equal in length but are not squares? If such a figure exists, can you construct it?

CBSE Important Questions Class 6 Maths Chapter 8 – Playing with Constructions

Q1. In a magical forest, two trees, Tree A and Tree B, are planted on the ground. A treasure has been placed at a point such that it is equidistant from both trees. Can you tell which of the given maps correctly depicts the position of the treasure?

(a)

Option (a): treasure 4 m from Tree A and 5 m from Tree B

(b)

Option (b): treasure 2 m from Tree A and 5 m from Tree B

(c)

Option (c): treasure 5 m from Tree A and 5 m from Tree B

(d)

Option (d): treasure 5 m from Tree A and 3 m from Tree B

Answer: (c)
'Equidistant' means at the same distance from both points. So the treasure must be at an equal distance from Tree A and from Tree B.
All such points lie on one special line called the perpendicular bisector of the line joining Tree A and Tree B. This line cuts the joining line exactly in the middle at a right angle.
In option (a) the distances are 4 m and 5 m, in option (b) they are 2 m and 5 m, and in option (d) they are 5 m and 3 m, so these are not equal. Only in option (c) both distances are 5 m.

Q2. Draw the following shapes:
(i)

Shape (i): a tilted square with two shaded arcs

(ii)

Shape (ii): a square inside a circle with the gaps shaded

Answer: (i) Steps:
Step 1: Draw a square of side 2 cm turned at 45° to the horizontal line, and name it ABCD anti-clockwise starting from the top.

Step 1: tilted square ABCD of side 2 cm

Step 2: Extend the lines from point C by 1 cm each and name the ends X and Y.

Step 2: lines extended 1 cm from C to points X and Y

Step 3: Open the compass to 1 cm. With C as the centre, draw an arc joining X and Y.

Step 3: arc of radius 1 cm drawn from centre C

Step 4: Now set the compass to 2 cm. With the same centre C, draw an arc joining B and D.

Step 4: arc of radius 2 cm drawn from centre C

Step 5: Shade the region between the two arcs to get the required figure.

Step 5: the completed shaded figure

(ii) Steps:
Step 1: Draw a square of side 2 cm and name it ABCD.

Step 1: square ABCD of side 2 cm

Step 2: Find the midpoints of the sides and mark where they cross. This point is the centre of the square.

Step 2: centre of the square marked

Step 3: Put the compass point on the centre and draw a circle passing through all four corners of the square.

Step 3: circle drawn through the four corners

Step 4: Shade the region between the square and the circle to get the required figure.

Step 4: the completed shaded figure

Q3. Identify which of the following can be constructed and how they may look if they can be constructed.
(i) A 4-sided figure having one pair of opposite sides equal and two angles of 90°.
(ii) A 4-sided figure whose all angles are 90° but opposite sides are not equal.

Answer: (i) It cannot be constructed.
If a 4-sided figure has two angles of 90° and one pair of opposite sides equal, then the other two angles must also become 90°. That makes it a rectangle, and in a rectangle both pairs of opposite sides are equal. So we cannot have a figure with exactly one pair equal.
(ii) It cannot be constructed.
If all four angles are 90°, the figure is a rectangle (a square is a special rectangle). In every rectangle the opposite sides are always equal, so the opposite sides cannot be unequal.

Q4. Construct a rectangle with sides 2 cm and 12 cm and check whether it satisfies the rectangle properties or not.

Answer: Step 1: Draw a horizontal line of 12 cm and name the end points A and B.

Step 1: line AB of length 12 cm

Step 2: Draw two lines of 2 cm each, perpendicular to AB from both ends, and name the ends C and D.

Step 2: perpendicular sides of 2 cm drawn from A and B

Step 3: Join C and D to complete the rectangle ABCD.
The rectangle ABCD satisfies all the properties of a rectangle:
• Opposite sides are equal (12 cm and 12 cm, 2 cm and 2 cm).
• All four angles are right angles.
• The two diagonals are equal in length.

The completed rectangle of 2 cm by 12 cm

Q5. Create two different rotated squares.

Answer: Square 1: Draw a square of side 4 cm and label the corners A, B, C and D in clockwise order. Now turn it about its centre so that the corners move to the top, bottom, left and right. Label the turned square A'B'C'D'.

A 4 cm square ABCD and its rotated form

Square 2: Draw another square of side 3 cm and label the corners E, F, G and H in clockwise order. Rotate it 60° clockwise about its centre and label the turned square E'F'G'H'.
The size of a square never changes when it is rotated; only its position changes. By changing the side length and the angle of turn, we can make many different rotated squares.

A 3 cm square EFGH rotated 60 degrees clockwise

Q6. Read the following statements and choose the correct option from the choices given below:
Assertion (A): A diagonal divides the opposite angles of the rectangle into two equal parts.
Reason (R): Diagonals of a rectangle are of equal measure.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Answer: (d) A is false, but R is true.
In a rectangle each corner angle is 90°. A diagonal does not cut these angles into two equal 45° parts unless the rectangle is a square, so the Assertion is false.
A rectangle does have two diagonals that are equal in length, so the Reason is true.

Q7. Read the following statements and choose the correct option from the choices given below:
Assertion (A): Construction of a circle requires two parameters: centre and its radius.
Reason (R): A compass can be used to construct a circle and its parts.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.
To draw a circle we must know where its centre is and how far the circle goes from that centre, that is, its radius. So the Assertion is true.
A compass is the tool made exactly for this: we place its point at the centre and open it to the radius. So the Reason is true and it explains how the centre and radius are actually used.

Q8. To construct the given shape, which of the following will be utilised?
(a) Locating a point from the centre of the circular curve
(b) Constructing a circular arc of radius 6 cm
(c) Locating a point equidistant from two points
(d) Constructing a triangle using ruler

A triangle of side 6 cm with a semicircle on top

Answer: (c) Locating a point equidistant from two points
The shape is an equilateral triangle of side 6 cm with a semicircle on top. After drawing the 6 cm line segment, we must find the third corner of the triangle, which is 6 cm from both ends of that line. In other words, we have to locate a point that is at the same distance from two points.

Q9. Which of the following statements is true for the given rectangle?
(a) The given rectangle can be divided into three equal size squares.
(b) The given rectangle can be divided into two equal size squares.
(c) The given rectangle can be divided into six equal size squares.
(d) The given rectangle can be divided into four equal size squares.

Rectangle of 4 cm by 6 cm

Answer: (c) The given rectangle can be divided into six equal size squares.
The rectangle is 6 cm long and 4 cm wide. If we cut the 6 cm sides into 3 parts of 2 cm and the 4 cm sides into 2 parts of 2 cm, we get squares of side 2 cm.
Number of squares = 3 × 2 = 6

The rectangle divided into six squares of side 2 cm

Q10. Which of the given items are necessarily required to construct the following shape?
(a) compass and ruler
(b) protractor and divider
(c) divider and ruler
(d) compass and ruler and protractor

A rectangle with a semicircle on top

Answer: (a) compass and ruler
The shape is a rectangle with a semicircle above it.
A ruler is needed to draw the straight sides of the rectangle and to measure their lengths.
A compass is needed to draw the semicircle, because it keeps the same radius all the way round.
A protractor is not necessary, as the right angles can be made with the ruler and compass.

Q11. Construct a rectangle ABCD, when AB = 3 cm and AC = 5 cm.

Answer: We know that the opposite sides of a rectangle are equal and each angle is 90°.
Steps of construction:
Step 1: Construct a line segment AB of length 3 cm.
Step 2: Draw a line perpendicular to AB at B. Call this line l.
Step 3: With A as the centre, draw an arc of radius 5 cm. It cuts the line l at point C.
Step 4: Draw perpendiculars from A to AB and from C to BC, and label their meeting point D.
Step 5: Join ABCD to get the required rectangle.
By the Pythagoras property in the right-angled triangle ABC: AB2 + BC2 = AC2, so 9 + BC2 = 25, BC2 = 16 and BC = 4 cm. So the sides of the rectangle are 3 cm and 4 cm.

Rectangle ABCD constructed with AB = 3 cm and diagonal AC = 5 cm

Q12. To construct a rectangle PQRS, where PQ = 10 cm and QR = 6 cm, which of the following steps is incorrect?
Step 1: Draw a line PQ = 15 cm and an angle of 90° at point P. As vertex S is 8 cm away from vertex P, cut a line segment PS = 8 cm from this perpendicular ray at P.
Step 2: Point R is 15 cm and 8 cm away from point S and point Q, respectively.
Step 3: By taking radii as 8 cm and 15 cm, draw arcs from points S and Q, respectively. These will intersect each other at point R.
Step 4: Join R to S and Q. PQRS is the required rectangle.
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4

Answer: (c) Step 3
In a rectangle the opposite sides are equal. Since PQ = 10 cm, SR must also be 10 cm, and since QR = 6 cm, PS must also be 6 cm.
To find R, the arc from S should have a radius of 10 cm and the arc from Q should have a radius of 6 cm.
Step 3 uses 8 cm and 15 cm instead, which are the wrong lengths. So Step 3 is incorrect.

Related Study Material on Extramarks

CBSE Important Questions for Class 6 Maths

Chapter 1 - Knowing Our Numbers

Chapter 2 - Whole Numbers

Chapter 3 - Playing with Numbers

Chapter 4 - Basic Geometrical Ideas

Chapter 5 - Understanding Elementary Shapes

Chapter 6 - Integers

Chapter 7 - Fractions

Chapter 9 - Data Handling

Chapter 10 - Mensuration

Chapter 11 - Algebra

Chapter 12 - Ratio and Proportion

Chapter 13 - Symmetry

Chapter 14 - Practical Geometry

FAQs (Frequently Asked Questions)

Playing with Constructions is a Class 6 Maths chapter on drawing accurate figures using a ruler and compass. It covers circles, squares, rectangles, diagonals and equal-distance constructions.

A compass draws circles, arcs and equal-distance marks. It helps students locate points accurately without repeated trial and error.

Draw one side, make perpendiculars at its endpoints, mark equal side lengths and join the remaining points. The final figure must have equal sides and four right angles.

A rectangle has equal opposite sides and all four angles equal to 90°. These two properties help students verify rectangle constructions.

Yes, the diagonals of a rectangle are equal in length. Students can verify this by constructing a rectangle and measuring both diagonals.