CBSE Class 6 Mathematics Playing with Constructions Practice Paper Worksheet Set 02 with Answers

This is CBSE Class 6 Maths Ganita Prakash Chapter 8 Playing with Constructions Practice Paper 29, a 40-mark test of 20 questions in Sections A to E, given here with step-by-step answers and accurate construction diagrams. It tests constructing a square of side 6 cm and a rectangle of 6 cm by 4 cm with ruler and compass, keeping the compass opening fixed, dividing a square into four equal squares and an 8 cm by 4 cm rectangle into equal squares, and using the diagonals of a square to find its centre and draw a circle inside it.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Construct a square when one side is given as 6 cm.
Answer:
Steps of construction:
Step 1: Draw a line segment PQ = 6 cm with a ruler.
Step 2: Draw perpendiculars to PQ at P and at Q (angle of 90° at both ends).
Step 3: Open the compass to 6 cm. With P as centre, cut the perpendicular at P at R; with Q as centre, cut the perpendicular at Q at S.
Step 4: Join RS. PQSR is the required square of side 6 cm.

In simple words: Draw one side, stand perpendiculars at its ends, cut 6 cm on each with the compass and join the tops.

Teacher's Note:
1. Keep the compass at 6 cm for both arcs.
2. Check: RS should also measure 6 cm and the angles at R and S should be 90°.

Question 12. A robot, while constructing a square ABCD, draws AB and the perpendicular at A but cuts an unequal length on it. Identify the mistake and the correction.
Answer:
Mistake: The length cut on the perpendicular at A is not equal to AB, so the compass opening used was different from the length of AB. The four sides will not all be equal and the figure will not be a square.
Correction: Set the compass opening exactly equal to AB, keep it fixed, and with A as centre cut the perpendicular at D so that AD = AB. Do the same at B to get C, then join DC.
In simple words: In a square all sides are equal, so the compass must cut the same length as AB.

Teacher's Note:
1. The robot's right angle is correct; only the length is wrong.
2. One compass opening should be used for all four sides of a square.

Question 13. Write the steps to extend one square into a strip of squares.
Answer:
Step 1: Extend the base of the square in a straight line.
Step 2: Open the compass equal to the side of the square and keep it fixed. Mark equal lengths along the extended base.
Step 3: Draw a perpendicular at each mark.
Step 4: Extend the top side and cut it with the same perpendiculars. Each new box is a square of the same size, giving a strip of equal squares.

In simple words: Mark the same side length again and again along the base and draw a perpendicular at each mark.

Teacher's Note:
1. The compass opening must not change while marking.
2. A strip of 3 squares of side 2 cm is a 6 cm by 2 cm rectangle.

Question 14. Write the steps to verify a constructed square.
Answer:
Step 1: Measure all four sides with a ruler. All four sides must be equal.
Step 2: Check each corner with a protractor or set square. All four angles must be 90°.
Step 3 (extra check): Measure the two diagonals; in a square they are equal.
In simple words: A square is correct only if all its sides are equal and all its angles are right angles.

Teacher's Note:
1. Equal sides alone are not enough; the angles must also be checked.
2. The compass can also be used to compare side lengths quickly.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Construct a rectangle when its length is 6 cm and breadth is 4 cm given.
Answer:
Steps of construction:
Step 1: Draw PQ = 6 cm (the given length).
Step 2: Draw perpendiculars to PQ at P and at Q.
Step 3: Open the compass to 4 cm. With P as centre cut the perpendicular at P at R; with Q as centre cut the perpendicular at Q at S.
Step 4: Join RS. PQSR is the required rectangle with length 6 cm and breadth 4 cm.

In simple words: Draw the 6 cm side, put perpendiculars at both ends, cut 4 cm on each and join.

Teacher's Note:
1. Check that RS also measures 6 cm.
2. Opposite sides of a rectangle are equal and all angles are 90°.

Question 16. Construct a square and divide it into four equal smaller squares.
Answer:
Take, for example, a square of side 6 cm.
Step 1: Construct square ABCD with AB = 6 cm using ruler and compass (side, perpendiculars at both ends, cut 6 cm on each, join).
Step 2: Draw both diagonals lightly; they meet at the centre O.
Step 3: Mark the mid-point of each side (3 cm from a corner). Join the mid-points of AB and DC, and of AD and BC; both lines pass through O and are perpendicular to the sides.
Step 4: The square is now divided into four equal squares, each of side 3 cm.

In simple words: Find the centre with the diagonals and draw two lines through it parallel to the sides.

Teacher's Note:
1. Each small square has side half of the big square's side.
2. The two dividing lines cross at the centre O at right angles.

Question 17. Construct a square and draw a circle inside it.
Answer:
Take, for example, a square of side 6 cm and a circle of radius 2 cm.
Step 1: Construct square ABCD of side 6 cm using ruler and compass.
Step 2: Draw both diagonals AC and BD lightly. They meet at O, the centre of the square.
Step 3: Open the compass to 2 cm, place its point at O and draw the circle. The circle lies inside the square with its centre at the centre of the square.

In simple words: Find the centre of the square with its diagonals and draw the circle from there.

Teacher's Note:
1. The radius must be at most half the side (3 cm here) for the circle to stay inside.
2. With radius exactly 3 cm the circle touches all four sides.

Section D: Long Answer Question (5 Marks)

Question 18. Construct a rectangle 8cm by 4cm and divide it into equal squares.
Answer:
Steps of construction:
Step 1: Draw the length PQ = 8 cm.
Step 2: Draw perpendiculars to PQ at P and at Q.
Step 3: With the compass opened to 4 cm, cut both perpendiculars at R and S, and join RS. PQSR is the 8 cm by 4 cm rectangle.
Step 4: The breadth is 4 cm, so each square must have side 4 cm. Number of squares = 8 ÷ 4 = 2. Keep the compass at 4 cm and mark M on PQ and N on RS, 4 cm from P and from R.
Step 5: Join MN; it is perpendicular to PQ. The rectangle is divided into 2 equal squares, each of side 4 cm.

In simple words: The breadth 4 cm fits twice in the length 8 cm, so one line in the middle makes two 4 cm squares.

Teacher's Note:
1. Number of squares = length ÷ breadth when the breadth divides the length exactly.
2. Check each part: all sides 4 cm and all angles 90°.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: A school stage is to be built in the shape of a square. One side is drawn first. Perpendiculars are constructed at both ends, and equal lengths are marked to complete the square. Diagonals are drawn to locate the centre, where a circular design is added using a compass.
Based on the above, answer the following questions:
(a) What construction is done after drawing the first side?
(b) How are equal sides ensured?
(c) Which construction locates the centre?
(d) What action is taken before drawing the circle?
Answer:
(a) Perpendiculars are drawn at both ends of the first side, so that the corners are right angles.
(b) By cutting equal lengths with the compass: the compass is opened to the length of the first side and kept fixed while marking the other sides.
(c) Drawing both diagonals; their meeting point is the centre of the square.
(d) The compass point is fixed at the centre (the meeting point of the diagonals) and the opening is set to the radius and kept fixed.
In simple words: Side, perpendiculars, equal lengths with a compass, diagonals for the centre, then the circle.

Teacher's Note:
1. The same order of steps works for any square.
2. The circle stays inside only if the radius is not more than half the side.

Question 20. Case Study 2: A classroom floor is rectangular. To tile it with equal square tiles, workers mark equal lengths along one side, draw perpendiculars at each mark, and extend lines across the rectangle. They check alignment and repeat the process until the floor is completely tiled.
Based on the above, answer the following questions:
(a) What is done after marking equal lengths?
(b) How are right angles maintained?
(c) How is the square pattern extended?
(d) What check ensures accurate square formation?
Answer:
(a) A perpendicular is drawn at each mark and extended across the rectangle.
(b) By constructing perpendicular lines (90° to the side) at every mark.
(c) By repeating the same two steps: marking equal lengths and drawing perpendiculars, row after row.
(d) Checking that every tile has equal sides and right-angled corners.
In simple words: Equal marks plus perpendiculars, repeated, give a grid of equal squares.

Teacher's Note:
1. Equal lengths give equal sides; perpendiculars give right angles.
2. A square needs both checks, not just one.