Class 6 Mathematics

Chapter 8 Solutions — Playing with Constructions

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Solutions

Overview

Step-by-step NCERT solutions for Playing with Constructions (Chapter 8, NCERT Class 6 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Playing with Constructions textbook chapter.

Solved

What these solutions cover

All 19 questions in Playing with Constructions are solved in the PDF. Here's what's inside, exercise by exercise:

Artwork

What radius should be taken in the compass to get this half circle (for the Wavy Wave with central line AB = 8 cm)? What should be the length of AX?

Squares and Rectangles

Which of the following is NOT a name for the square with corners S (top-left), P (top-right), Q (bottom-right), R (bottom-left)? 1. PQSR 2. SPQR 3. RSPQ 4. QRSP
Identify if there are any squares in this collection (figures A, B, C, D drawn on a dot grid). Use measurements if needed.

Constructing Squares and Rectangles

Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.
Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both the rectangle properties.
Is it possible to construct a 4-sided figure in which all the angles are equal to 90° but opposite sides are not equal?

An Exploration in Rectangles

In rectangle ABCD with AB = 7 cm and BC = 4 cm, X is on side AD and Y is on side BC. Fill in the table: When X is 5 mm away from A and Y is 3 cm away from B, XY = ___ cm ___ mm. When X is 1 cm away from A and Y is 1 cm away from B, XY = ___ cm ___ mm. When X is 2 cm away from A and Y is 4 cm away from B, XY = ___ cm ___ mm.
2.
When X and Y are placed at the same distance from A and B respectively (5 mm each; 1 cm each; 1 cm 5 mm each), find the length of XY in each case. What do you observe about
- (i) how XY compares to AB, and
- (ii) the shape of figure ABYX?
How does the farthest distance between X and Y compare with the length of AC and BD (the diagonals of rectangle ABCD)?
Construct a rectangle that can be divided into 3 identical squares. Give the lengths of the sides.
5.
Give the lengths of the sides of a rectangle that cannot be divided into
- (a) two identical squares;
- (b) three identical squares.
A Square within a Rectangle: Construct a rectangle of sides 8 cm and 4 cm. Construct a square inside it such that the centre of the square is the same as the centre of the rectangle.

Exploring Diagonals of Rectangles and Squares

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?
Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.
Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?
Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.

Points Equidistant from Two Given Points

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

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