Class 6 Maths Chapter 8 Extra Questions Playing with Constructions
Class 6 Maths Playing with Constructions Extra Questions
NCERT Class 6 Maths Chapter 8 Playing with Constructions Extra Questions and Answers
Question 1.
Construct a circle of diameter 5 cm.
Solution:
Steps of construction:
(i) Draw a line segment AB of length 5 cm.
(ii) Mark a midpoint O of line segment AB using ruler.
(iii) Taking centre at O and by opening the compass equal to OA or OB, draw a circle.
Thus, it is required circle.
Question 2.
Construct a rectangle having adjacent sides of 6 cm and 4 cm and find its area.
Solution:
Given: Adjacent sides are 6 cm and 4 cm.
Steps for construction:
Step 1: Draw a rough diagram and mark the given measurements.
Step 2: Draw a line segment AB = 6 cm.
Step 3: At A, using a protractor draw AX JL AB.
Step 4: With A as centre, draw an arc of radius 4 cm and let it cut AX at D.
Step 5: With D as centre, draw an arc of radius 6 cm above the line segment AB.
Step 6: With B as centre, draw an arc of radius 4 cm cutting the previous arc at C. Join BC and CD. Thus, ABCD is the required rectangle.
Area of Rectangle = length × breadth
= 6 cm × 4 cm = 24 sq cm
Question 3.
Construct a square of side 5 cm.
Solution:
Steps for construction:
Step 1: Draw a line segment AB of length 5 cm.
Step 2: Mark a point to draw a perpendicular to AB through A.
Step 3: Using a ruler mark D on the perpendicular such that AD = 5 cm.
Step 4: Draw a perpendicular to line segment AB through B.
Step 5: Using a ruler mark C on the perpendicular such that BC = 5 cm.
Step 6: Join C and D.
Thus, ABCD is the required square.
Question 4.
Which of the following are squares and rectangles in the given collection?
Solution:
Figures A and C are rectangles, as in both figures, opposite sides are equal in length by counting the number of dots between the comers. Also, each angle is 90° in each of the figures.
Figures B and D are squares, as in both figures, the length of each side is equal. Also, each angle is 90° in both the figures.
Question 5.
Construct a rectangle ABCD in which side AB = 3 cm and diagonal AC = 5 cm.
Solution:
Given, for a rectangle, side AB = 3 cm and diagonal AC = 5 cm.
Steps of construction:
(i) Draw the base AB of length 3 cm.
(ii) Draw a perpendicular to line AB at the point B. Let us name this line as m.
(iii) Using a ruler, take the distance of 5 cm in a compass and from point A, mark an arc cutting line m at C. Join AC.
(iv) Construct perpendicular to AB and BC at points A and C respectively. The point where these perpendiculars intersect is the fourth point D.
Thus, ABCD is the required rectangle.
Question 6.
In the figure, given that NT = \(\frac{1}{2}\)MT. Find the radius of the half circle shown in the figure.
Solution:
Given that, the diameter NT of the half circle is half the length of the line segment MT.
So, NT = \(\frac{1}{2}\)MT = \(\frac{12 \mathrm{~cm}}{2}\) = 6 So, radius of the half circle = half the length of the line segment NT
= \(\frac{6}{2}\) cm
= 3 cm
