## 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