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Class 6 Maths: Playing with Constructions, 8 practice questions with answers

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These are 8 practice questions on Chapter 8, Playing with Constructions, of the new NCERT Class 6 Maths textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover a circle as the points at one distance from a centre, naming a shape by its corners, constructing a square, the nearest and farthest points across a rectangle, a shape built from identical squares, a rectangle centred in another, a rectangle from one side and its diagonal, and the angles a diagonal makes. Every construction comes with lengths you can check with a ruler, to the nearest millimetre. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, and none of the chapter's own figures, worked examples or exercise settings is reused, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 6, Chapter 8, printed pages 187 to 216):

Circles and rectangles

Question 1. A goat is tied to a peg in a field with a rope 3.5 m long. A tulsi plant grows 3 m from the peg and a rose bush 4.2 m from it. (a) Which of the two can the goat reach? (b) What shape is the edge of the patch it can reach, and where is its centre? (c) The goat bites two leaves at the very edge of its reach. How far apart can they be at most? Draw the patch to scale, 1 cm for 1 m.

Answer: (a) only the tulsi; (b) a circle of radius 3.5 m with the peg at its centre; (c) 7 m. (a) With the rope pulled tight, the goat reaches every spot exactly 3.5 m from the peg, and anything nearer. The tulsi, at 3 m, is within reach; the rose bush, at 4.2 m, is 0.7 m too far. (b) All the farthest spots are the same distance, 3.5 m, from the peg, so they form a circle: the peg is its centre and the rope's length is its radius. On paper, open the compass to 3.5 cm and draw the circle around a point for the peg. (c) Two points on the circle are farthest apart when they are on opposite sides of the centre: 3.5 + 3.5 = 7 m (7 cm on your drawing). (Circles, centre and radius, pages 188 and 189.)

Question 2. A flower bed has five straight sides, and its corners, in order going round it, are P, Q, R, S and T. (a) Is TSRQP a correct name for it? Is PRQST? (b) How many correct names does it have in all? (c) How many would a six-sided bed have?

Answer: (a) TSRQP yes, PRQST no; (b) 10; (c) 12. The rule is the same as for a rectangle: a correct name lists the corners in the order you meet them as you go round, starting from any corner and going either way. (a) TSRQP starts at T and goes round backwards, so it is correct. PRQST jumps from P to R, but the corner after P is Q, so it is not. (b) There are 5 corners to start from and 2 directions to go, so 5 × 2 = 10 names. (c) 6 starting corners and 2 directions give 6 × 2 = 12. (Naming a shape by going round its corners, page 193.)

Question 3. A square handkerchief needs exactly 22 cm of lace to go once round its edge. Find the length of its side, construct it full size, and say what each diagonal should measure.

Answer: side 5.5 cm; each diagonal about 7.8 cm, and the two are equal. A square has 4 equal sides, so each side is 22 ÷ 4 = 5.5 cm. Draw KL = 5.5 cm. At K, draw a line perpendicular to KL and mark N on it 5.5 cm from K; at L, draw a perpendicular and mark M 5.5 cm from L, on the same side. Join MN and check that it is also 5.5 cm. The diagonals KM and LN should each measure about 7.8 cm. (Constructing squares and rectangles, pages 195 and 196; diagonals, page 203.)

Question 4. Two straight wires, each 9 cm long, are fixed parallel to each other, 5 cm apart, with their ends in line. A bead slides on each wire. (a) What is the shortest possible distance between the beads, and where must they be? (b) What is the longest, and where must they be? (c) Draw the wires to scale and check both by measuring.

Answer: (a) 5 cm, whenever one bead is straight across from the other; (b) about 10.3 cm, when they are at opposite ends of the two wires. Join the ends of the wires: they make a rectangle 9 cm by 5 cm, with the wires as its long sides. (a) When the beads are straight across from each other, the line joining them is perpendicular to both wires and is as long as the gap, 5 cm. Move either bead along and the line slants, so it gets longer. (b) The line is longest when it slants the most: one bead at the left end of its wire and the other at the right end of the other wire. The line joining them is then a diagonal of the rectangle, which measures about 10.3 cm. (Moving points along two sides of a rectangle, pages 197 to 199.)

Planning constructions

Question 5. Four identical squares, each of side 3.5 cm, are put together to make a T: three in a row along the top and one under the middle square. (a) Draw a rough diagram. How long is the top edge of the T, and how tall is the T? (b) How many sides does the outline have, and what is its perimeter? (c) Construct the T.

Answer: (a) top edge 10.5 cm, height 7 cm; (b) 8 sides, perimeter 35 cm. (a) The top edge runs along three squares: 3 × 3.5 = 10.5 cm. The T is two squares tall: 2 × 3.5 = 7 cm. (b) Going round the outline: the top edge (10.5 cm), the right end of the bar (3.5 cm), the underside of the right arm (3.5 cm), the right side of the stem (3.5 cm), the bottom of the stem (3.5 cm), the left side of the stem (3.5 cm), the underside of the left arm (3.5 cm) and the left end of the bar (3.5 cm). That is 8 sides, and 10.5 + 7 × 3.5 = 35 cm. (c) Construct a 10.5 cm by 3.5 cm rectangle for the bar. Mark the points 3.5 cm and 7 cm along its bottom edge, draw perpendiculars down from them, mark 3.5 cm on each and join the two marks. (Rough diagrams and building shapes from squares, pages 199 to 201.)

Question 6. A photo 9 cm long and 6 cm wide is stuck exactly in the middle of a card 15 cm long and 10 cm wide. (a) How wide is the border on the left and right, and at the top and bottom? (b) Construct the card and the photo. (c) Draw both diagonals of the card and of the photo. What do you notice?

Answer: (a) 3 cm on the left and right, 2 cm at the top and bottom; (c) all four diagonals pass through the same point. (a) Along the length, 15 − 9 = 6 cm is left over, shared equally: 3 cm on each side. Across, 10 − 6 = 4 cm is left over: 2 cm at the top and at the bottom. (b) Construct the 15 cm by 10 cm card. Mark points 3 cm in from each short side along the top and bottom edges, and 2 cm in from each long side along the two short sides; perpendiculars from these marks meet at the photo's four corners. (c) The diagonals of the card and of the photo all cross at one point, the centre of both, which is what "in the middle" means. (A shape centred inside a rectangle, pages 201 and 202; diagonals, page 203.)

From diagonals

Question 7. A phone screen is a rectangle 6 cm wide, and its diagonal is 7.5 cm. Construct the screen full size, give the steps, and measure its height.

Answer: the height is about 4.5 cm. Draw the bottom edge EF = 6 cm. At F, draw a line perpendicular to EF. The top corner G above F is on this line and 7.5 cm from E, so open the compass to 7.5 cm and draw an arc from E; it cuts the line at G. Draw a perpendicular to EF at E and a perpendicular to FG at G; they meet at the fourth corner H. Measuring FG (and EH) gives about 4.5 cm, and the other diagonal, FH, also measures 7.5 cm. (A rectangle from a side and a diagonal, pages 208 to 210.)

Question 8. Construct a rectangle 12 cm long and 5 cm wide and draw one diagonal. (a) Measure the diagonal. (b) The diagonal makes two angles at each of the two corners it joins. Measure all four. Which are equal, and what do the two angles at one corner add up to? (c) Would the angles change for a rectangle twice as long and twice as wide?

Answer: (a) 13 cm; (b) about 23° and 67° at each end: the two 23° angles are equal, the two 67° angles are equal, and the pair at each corner adds up to 90°; (c) no. (a) The diagonal measures 13 cm. (b) At each end, the diagonal makes an angle of about 23° with the long side and about 67° with the short side. At each corner the two angles together fill the right angle: 23° + 67° = 90°. (c) A rectangle 24 cm by 10 cm is the same shape, only larger, so its diagonal leans the same way and the angles stay about 23° and 67°; only the lengths double. (The angles a diagonal makes in a rectangle, pages 205 to 207.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 186 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.