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

Practice Paper 30 for CBSE Class 6 Mathematics Ganita Prakash Chapter 8 Playing with Constructions is a complete 40-mark paper of 20 questions in five sections (A to E), solved step by step with exact ruler-and-compass diagrams. The questions cover copying a 6 cm line segment, drawing a perpendicular at a point, constructing an 8 cm square, rectangles of 8 cm by 4 cm and 8 cm by 2 cm, a rectangle from one side (5 cm) and a diagonal (7 cm), and dividing a square into four squares with a circle in each.

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 8 cm.
Answer:
Steps of construction:
Step 1: Draw PQ = 8 cm with a ruler.
Step 2: Draw perpendiculars to PQ at P and at Q.
Step 3: Open the compass to 8 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 8 cm.

In simple words: Draw an 8 cm side, raise perpendiculars at both ends, cut 8 cm on each and join.

Teacher's Note:
1. Keep the compass at 8 cm throughout.
2. Check RS = 8 cm and the top angles are 90°.

Question 12. Write the steps of Constructions to construct a line segment AB of length 6 cm and copy it using compass.
Answer:
Step 1: Draw a line segment AB = 6 cm with a ruler.
Step 2: Place the compass point at A and open it until the pencil tip is exactly on B. The opening is now 6 cm.
Step 3: Draw a line l and mark a point C on it.
Step 4: Without changing the opening, place the compass point at C and draw an arc cutting l at D.
Step 5: CD is the copy of AB, so CD = AB = 6 cm.

In simple words: The compass picks up the length of AB and puts the same length down on the new line.

Teacher's Note:
1. Check by measuring CD with a ruler.
2. Copying with a compass avoids reading errors on the ruler.

Question 13. Write the steps of Constructions to construct perpendicular line at point A on line segment AB.
Answer:
Step 1: Draw the line segment AB and extend it a little beyond A.
Step 2: With A as centre and any small radius, draw arcs cutting the line on both sides of A at P and Q (so AP = AQ).
Step 3: With P and Q as centres and a radius greater than AP, draw two arcs that cut each other at R.
Step 4: Join AR and extend it. AR is perpendicular to AB, that is, ∠RAB = 90°.

In simple words: Mark two points equally far from A on the line, then find a point equally far from both of them; the line through it and A stands straight up.

Teacher's Note:
1. Use the same radius for both arcs in Step 3.
2. Check the angle at A with a protractor; it should be 90°.

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

Teacher's Note:
1. Unlike a square, a rectangle need not have all four sides equal.
2. Equal diagonals are a quick test of the right angles.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Construct a square, divide it into four equal smaller squares and then construct four circles inside each square.
Answer:
Take, for example, a square of side 8 cm and circles of radius 1.2 cm.
Step 1: Construct square ABCD with AB = 8 cm using ruler and compass.
Step 2: Draw both diagonals lightly; they meet at the centre O.
Step 3: Mark the mid-point of each side (4 cm from a corner) and join the mid-points of opposite sides. The two lines pass through O and divide ABCD into four squares of side 4 cm.
Step 4: In each small square draw its diagonals lightly to find its centre.
Step 5: Open the compass to 1.2 cm and draw a circle at the centre of each small square. Four equal circles now sit inside the four equal squares.

In simple words: Split the square into four with two lines through its centre, then draw a circle from the centre of each part.

Teacher's Note:
1. The radius must not exceed half the small side (2 cm here).
2. Keep one compass opening so all four circles are equal.

Question 16. Construct a rectangle where one of its sides is 5 cm and the length of a diagonal is 7 cm.
Answer:
Steps of construction:
Step 1: Draw DC = 5 cm.
Step 2: Draw a perpendicular to DC at C.
Step 3: With D as centre and radius 7 cm, draw an arc cutting the perpendicular at B. Then DB = 7 cm is the diagonal.
Step 4: With D as centre and radius equal to CB, draw an arc above D.
Step 5: With B as centre and radius 5 cm, draw an arc cutting the previous arc at A.
Step 6: Join AB and AD, and also the diagonal BD. ABCD is the required rectangle with DC = 5 cm and diagonal BD = 7 cm.
On measuring, the other side BC comes out to be about 4.9 cm.

In simple words: Draw the 5 cm side, raise a perpendicular, and let a 7 cm arc from the other end decide how tall the rectangle is.

Teacher's Note:
1. The diagonal (7 cm) must be longer than the side (5 cm), or the arc will not reach the perpendicular.
2. Check: the second diagonal AC should also measure 7 cm.

Question 17. Construct a rectangle when its length is 8 cm and breadth is 4 cm given.
Answer:
Steps of construction:
Step 1: Draw PQ = 8 cm (the given length).
Step 2: Draw perpendiculars to PQ at P and at Q.
Step 3: Open the compass to 4 cm and cut the perpendiculars at R (centre P) and S (centre Q).
Step 4: Join RS. PQSR is the required rectangle of length 8 cm and breadth 4 cm.

In simple words: Draw the 8 cm side, put perpendiculars at its ends, cut 4 cm on each and join.

Teacher's Note:
1. Check that RS = 8 cm.
2. Both perpendiculars must get the same 4 cm cut, or the top side will slant.

Section D: Long Answer Question (5 Marks)

Question 18. Construct a rectangle 8cm by 2cm 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 2 cm, cut both perpendiculars at R and S, and join RS. PQSR is the 8 cm by 2 cm rectangle.
Step 4: Each square must have side 2 cm (the breadth). Number of squares = 8 ÷ 2 = 4. Keeping the compass at 2 cm, mark points every 2 cm along PQ and along RS (at 2 cm, 4 cm and 6 cm from the left end).
Step 5: Join the matching marks; these lines are perpendicular to PQ. The rectangle is divided into 4 equal squares, each of side 2 cm.

In simple words: The breadth 2 cm fits 4 times in the length 8 cm, so three lines make four 2 cm squares.

Teacher's Note:
1. Number of squares = length ÷ breadth = 8 ÷ 2 = 4.
2. Mark from the same end each time so the gaps stay equal.

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

Question 19. Case Study 1: Riya is designing a square garden using tiles. She constructs a square using compass and ruler so that all tiles are equal. She starts by drawing one side and then constructs perpendicular lines at both ends. Using compass, she marks equal lengths and completes the square. Later, she divides the garden into four equal square sections using perpendicular lines through the center. This helps her plant different flowers in each section equally. Proper compass use ensures accurate construction.
Based on the above, answer the following questions:
(a) Which instrument ensures equal sides?
(b) Why perpendicular lines are necessary?
(c) What shape is formed?
(d) How many smaller squares formed?
Answer:
(a) The compass; with a fixed opening it marks the same length for every side.
(b) Perpendicular lines make right angles (90°) at the corners, which every square needs.
(c) A square (the garden).
(d) Four equal smaller squares, made by the two perpendicular lines through the centre.
In simple words: Compass for equal sides, perpendiculars for right angles, giving a square cut into 4 squares.

Teacher's Note:
1. Two lines through the centre, parallel to the sides, always give 4 equal squares.
2. Each small square has side half of the garden's side.

Question 20. Case Study 2: A carpenter constructs rectangular floor using ruler and compass. He first draws the length and constructs perpendicular lines at both ends. Then he marks breadth and completes rectangle. To check accuracy, he measures opposite sides and angles. He confirms all angles are right angles and opposite sides equal. This ensures correct rectangular shape. Compass ensures accurate measurement and perpendicular construction helps form correct shape.
Based on the above, answer the following questions:
(a) What shape formed?
(b) How many right angles present?
(c) Which instrument ensures equal lengths?
(d) Which construction ensures right angle?
Answer:
(a) A rectangle.
(b) Four right angles, one at each corner.
(c) The compass, used with a fixed opening.
(d) Constructing perpendicular lines at the ends of the length.
In simple words: The floor is a rectangle with four right angles; the compass fixes lengths and perpendiculars fix angles.

Teacher's Note:
1. A rectangle has opposite sides equal and all four angles 90°.
2. Checking both sides and angles confirms the shape.