Mensuration (Exercise 20.3) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

 Page 1


 
 
 
 
 
 
                                                                           
1. The following figures are drawn on a squared paper. Count the number of squares enclosed by each 
figure and find its area, taking the area of each square as 1 cm
2
. (Fig. 20.25). 
 
Solution: 
 
(i) The given shape has 16 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 16 × 1 = 16 cm
2
 
 
(ii) The given shape has 36 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 36 × 1 = 36 cm
2
 
 
(iii) The given shape has 15 complete and 6 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 15 + 6 × 12 = 18 cm
2
 
 
(iv) The given shape has 20 complete and 8 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 20 + 8 × 12 = 24 cm
2
 
 
(v) The given shape has 13 complete, 8 more than half and 7 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 13 + 8 × 1 = 21 cm
2
 
 
(vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 8 + 6 × 1 = 14 cm
2
 
 
2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the 
approximate area of each by counting the number of squares complete, more than half and exactly half. 
Page 2


 
 
 
 
 
 
                                                                           
1. The following figures are drawn on a squared paper. Count the number of squares enclosed by each 
figure and find its area, taking the area of each square as 1 cm
2
. (Fig. 20.25). 
 
Solution: 
 
(i) The given shape has 16 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 16 × 1 = 16 cm
2
 
 
(ii) The given shape has 36 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 36 × 1 = 36 cm
2
 
 
(iii) The given shape has 15 complete and 6 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 15 + 6 × 12 = 18 cm
2
 
 
(iv) The given shape has 20 complete and 8 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 20 + 8 × 12 = 24 cm
2
 
 
(v) The given shape has 13 complete, 8 more than half and 7 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 13 + 8 × 1 = 21 cm
2
 
 
(vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 8 + 6 × 1 = 14 cm
2
 
 
2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the 
approximate area of each by counting the number of squares complete, more than half and exactly half. 
 
 
 
 
 
 
Solution: 
 
(i) A rectangle 
The given shape has 18 complete squares 
Assume that area of one square = 1 cm
2
 
So the area of the rectangle = 18 × 1 = 18 cm
2
 
 
 
(ii) A triangle 
The given shape has 4 complete, 6 more than half and 6 less than half squares. 
Assume that area of one square = 1 cm
2
 
So the area of the square = 4 + 6 × 1 = 10 cm
2
 
 
 
(iii) Any irregular figure 
The given shape has 10 complete, 1 exactly half, 7 more than half and 6 less than half squares. 
Assume that area of one square = 1 cm
2
 
So the area of the shape = 10 + 1 × 12 + 7 × 1 = 17.5 cm
2
 
 
Page 3


 
 
 
 
 
 
                                                                           
1. The following figures are drawn on a squared paper. Count the number of squares enclosed by each 
figure and find its area, taking the area of each square as 1 cm
2
. (Fig. 20.25). 
 
Solution: 
 
(i) The given shape has 16 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 16 × 1 = 16 cm
2
 
 
(ii) The given shape has 36 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 36 × 1 = 36 cm
2
 
 
(iii) The given shape has 15 complete and 6 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 15 + 6 × 12 = 18 cm
2
 
 
(iv) The given shape has 20 complete and 8 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 20 + 8 × 12 = 24 cm
2
 
 
(v) The given shape has 13 complete, 8 more than half and 7 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 13 + 8 × 1 = 21 cm
2
 
 
(vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 8 + 6 × 1 = 14 cm
2
 
 
2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the 
approximate area of each by counting the number of squares complete, more than half and exactly half. 
 
 
 
 
 
 
Solution: 
 
(i) A rectangle 
The given shape has 18 complete squares 
Assume that area of one square = 1 cm
2
 
So the area of the rectangle = 18 × 1 = 18 cm
2
 
 
 
(ii) A triangle 
The given shape has 4 complete, 6 more than half and 6 less than half squares. 
Assume that area of one square = 1 cm
2
 
So the area of the square = 4 + 6 × 1 = 10 cm
2
 
 
 
(iii) Any irregular figure 
The given shape has 10 complete, 1 exactly half, 7 more than half and 6 less than half squares. 
Assume that area of one square = 1 cm
2
 
So the area of the shape = 10 + 1 × 12 + 7 × 1 = 17.5 cm
2
 
 
 
 
 
 
 
 
3. Draw any circle on the graph paper. Count the squares and use them to estimate the area of the circular 
region. 
Solution: 
 
 
 
The given circles has 21 complete, 15 more than half and 8 less than half squares. 
Assume that area of one square = 1 cm
2
 
By neglecting less than half squares, we get 
Area of the circle = 21 + 15 = 36 cm
2
 
 
4. Use tracing paper and centimetre graph paper to compare the areas of the following pairs of figures: 
 
Solution: 
 
 
With the help of tracing paper trace both the figures on a graph 
Figure (i) has 4 complete, 9 more than half and 9 less than half squares. 
Assume that area of one square = 1 cm
2
 
By neglecting less than half squares, we get 
Area of the shape = 4 + 9 = 13 cm
2
 
 
Figure (ii) has 8 complete, 11 more than half and 10 less than half squares. 
Assume that area of one square = 1 cm
2
 
Page 4


 
 
 
 
 
 
                                                                           
1. The following figures are drawn on a squared paper. Count the number of squares enclosed by each 
figure and find its area, taking the area of each square as 1 cm
2
. (Fig. 20.25). 
 
Solution: 
 
(i) The given shape has 16 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 16 × 1 = 16 cm
2
 
 
(ii) The given shape has 36 complete squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 36 × 1 = 36 cm
2
 
 
(iii) The given shape has 15 complete and 6 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 15 + 6 × 12 = 18 cm
2
 
 
(iv) The given shape has 20 complete and 8 half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 20 + 8 × 12 = 24 cm
2
 
 
(v) The given shape has 13 complete, 8 more than half and 7 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 13 + 8 × 1 = 21 cm
2
 
 
(vi) The given shape has 8 complete, 6 more than half and 4 less than half squares. 
It is given that area of one square = 1 cm
2
 
So the area of the given shape = 8 + 6 × 1 = 14 cm
2
 
 
2. On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the 
approximate area of each by counting the number of squares complete, more than half and exactly half. 
 
 
 
 
 
 
Solution: 
 
(i) A rectangle 
The given shape has 18 complete squares 
Assume that area of one square = 1 cm
2
 
So the area of the rectangle = 18 × 1 = 18 cm
2
 
 
 
(ii) A triangle 
The given shape has 4 complete, 6 more than half and 6 less than half squares. 
Assume that area of one square = 1 cm
2
 
So the area of the square = 4 + 6 × 1 = 10 cm
2
 
 
 
(iii) Any irregular figure 
The given shape has 10 complete, 1 exactly half, 7 more than half and 6 less than half squares. 
Assume that area of one square = 1 cm
2
 
So the area of the shape = 10 + 1 × 12 + 7 × 1 = 17.5 cm
2
 
 
 
 
 
 
 
 
3. Draw any circle on the graph paper. Count the squares and use them to estimate the area of the circular 
region. 
Solution: 
 
 
 
The given circles has 21 complete, 15 more than half and 8 less than half squares. 
Assume that area of one square = 1 cm
2
 
By neglecting less than half squares, we get 
Area of the circle = 21 + 15 = 36 cm
2
 
 
4. Use tracing paper and centimetre graph paper to compare the areas of the following pairs of figures: 
 
Solution: 
 
 
With the help of tracing paper trace both the figures on a graph 
Figure (i) has 4 complete, 9 more than half and 9 less than half squares. 
Assume that area of one square = 1 cm
2
 
By neglecting less than half squares, we get 
Area of the shape = 4 + 9 = 13 cm
2
 
 
Figure (ii) has 8 complete, 11 more than half and 10 less than half squares. 
Assume that area of one square = 1 cm
2
 
 
 
 
 
 
 
By neglecting less than half squares, we get 
Area of the shape = 8 + 11 = 19 cm
2
 
 
By comparing the areas of both the shapes, we know that the figure (ii) has area greater than that of figure (i).