By using Ganita Prakash Book Class 6 Solutions and Chapter 8 Playing with Constructions Class 6 NCERT Solutions Question Answer, students can improve their problem-solving skills.
Class 6 Maths Chapter 8 Playing with Constructions Solutions
Playing with Constructions Class 6 Solutions Questions and Answers
8.1 Artwork Construct (Page No. 190 – 191)
Question 1.
What radius should be taken in the compass to get this half circle? What should be the length of AX?
Solution:
The radius should be taken of 2 cm in the compass to get this half circle and the length of AX is 4 cm.
Question 2.
Take a central line of a different length and try to draw the wave on it.
Solution:
Try it yourself
Question 3.
Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure ‘A Person’).
The challenge here’is to get both the waves to be identical. This may be tricky!
Solution:
To make waves smaller than the half circle, you should set the compass to a radius smaller than the one used for the circle waves.
8.2 Squares and Rectangles Figure it Out (Page 194)
Question 1.
Draw the rectangle and four squares configuration (shown in Fig. 8.3) on a dot paper.
What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.
Solution:
Draw a rectangle using four dots and draw four squares to make sure all the squares are equal in size and placed around the rectangle in symmetry.
Question 2.
Identify if there are any squares in this collection. Use measurements if needed.
Solution:
In the given collection, only figure A is square as all the sides are equal length and the vertex angles are 90°.
Question 3.
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.
Solution:
In all the squares, the sides are equal in length and all vertex angles are 90°.
In all the rectangles, the opposite sides are equal in length and each vertex angle is 90°.
8.3 Constructing Squares and Rectangles Construct (Page No. 197)
Question 1.
Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.
Solution:
Rectangle with sides 4 cm and 6 cm.
Steps
(i) Draw a,straight line AB = 6 cm using a ruler.
(ii) Place the protractor on point A and mark a 90° angle from AB.
(iii) Draw a line from A along this angle and measure AD 4 cm.
(iv) Repeat the same process at point B to draw a line BC perpendicular to AB and also 4 cm long.
(v) Join points D and C to complete the rectangle ABCD.
(vi) Verify that AB and CD are equal as well as AD and BC and all angles are 90°.
Question 2.
Draw a rectangle of sides 2 cm and 10 cm. After drawinfg, check if it satisfies both the rectangle properties. t
Solution:
Rectangle with sides 2 cm and 10 cm.
Steps
(i) Draw a line AB = 10 cm.
(ii) At point A, use the protractor to mark a 90° angle and draw line AD 2 cm.
(iii) Do the same at point B to draw line BC = 2 cm.
(iv) Connect D and C to complete the rectangle.
(v) Check that opposite side are equal and all angles are 90°.
Question 3.
Is it possible to construct a 4-sided figure in which
(i) all the angles are equal to 90°
(ii) opposite sides are not equal?
Solution:
No
8.5 Exploring Diagonals of Rectangles and Squares Construct (Page No. 211)
Question 1.
Construct a rectangle in which one of the diagonals <1 divides the opposite angles into 50° and 40°.
Solution:
Draw a horizontal line segment AB. This will be one side of the rectangle.
(i) At point A, use a protractor to measure and draw AX a 50° angle.
(ii) At point B, measure and draw a 90° angle. Draw a line segment BC extending from B at this angle meeting AX at C.
(iii) At Point A and C, draw a 90° angle which meets at the point D.
ABCD is the required rectangle. Here, diagonal AC divides the opposite angles A and C into 50° and 40°.
Question 2.
Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?
Solution:
Draw a horizontal line segment AB. This will be one side of the rectangle.
(i) At point A, use a protractor to measure and draw AX a 45° angle.
(ii) At point B, measure and draw a 90° angle. Draw a line segment BC extending from B at this angle meeting AX at C.
(iii) At Point A and C, Draw a 90° angle which meets at the point D.
ABCD is the required rectangle. Here, diagonal AC divides the opposite angles A and C into 45° and 45°.
Observation You will notice that when the diagonals divide the opposite angles into 45° and 45°, so the sides of the rectangle will be equal, forming a square.
Question 3.
Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
Solution:
Steps
(i) Draw a line segment AB = 4 cm.
(ii) At B, draw a perpendicular line BY.
(iii) Take an arc of length 7 cm on a compass and draw the arc to cut the perpendicular BY at the point C.
(iv) At the points C and A draw two perpendiculars which will intersects at the point D.
Here, ABCD is the required rectangle.
Question 4.
Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.
Solution:
Steps
(i) Draw a line segment AB = 3 cm.
(ii) At B, draw a perpendicular line BY.
(iii) Take an arc of length 7 cm on a compass and draw the arc to cut the perpendicular BY at the point C.
(iv) At the points C and A draw two perpendiculars which will intersects at the point D.
Here, ABCD is the required rectangle.
8.6 Points Equidistant from Two Given Points Construct (Page No. 215)
Question 1.
Construct a bigger house in which all the sides are of length 7 cm.
Solution:
Steps
(i) Draw a horizontal line DE of length 7 cm.
(ii) At point D, draw a perpendicular line upwards using your scale or set square. Measure 7 cm on this line and mark point B.
(iii) Similarly, at point E, draw a perpendicular line upwards and ma$k point C at a distance of 7 cm.
(iv) Using your compass, set a radius of length 7 cm. With B as the center, draw an arc. With the same radius, and C as the center, draw another arc to intersect the first arc. Mark this intersection as point A.
(v) Draw line segments AB and AC to complete the triangle.
(vi) With A as a centre and AB as radius draw an arc BC.
(vii) On the base DE, draw a rectangle of sides 2 cm and 1 cm.
Hence, ABDEC is the required house.
Question 2.
Try to recreate A Person’, ‘Wavy Wave’ and ‘Eyes’ from the section. Artwork, using ideas involved in the ‘House’ construction.
Solution:
Do it by yourself
Question 3.
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?
Solution:
Yes, there is a 4-sided figure where all sides are equal in length but is not a square. This figure is known as a rhombus.
Steps
(i) Draw a line segment AB of any length.
Let it will be 5 cm.
(ii) Draw any angle less than 90° at point A. Let will be 70°.
(iii) Mark the point D using ruler of length 5 cm and ray AX.
(iv) Now, draw two circles of radius 5 cm at point D and B and they will intersect at point C.
(v) Join BC and DC.
ABCD is required 4-sided figure.