## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 15 Data Handling Ex 15.2

ML Aggarwal Class 6 Solutions Chapter 15 Data Handling Ex 15.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 15 Data Handling Ex 15.2

Question 1.
Following pictograph shows the number of tractors in five villages.

Observe the pictograph and answer the following questions.
(i) Which village has the minimum number of tractors?
(ii) Which village has the maximum number of tractors?
(iii) How many more tractors village C has as compared to village B.
(iv) What is the total number of the tractor in all the five villages?
Solution:

Question 2.
The number of girl students in each class of a co-educational middle school is depicted by the pictograph.

Observe this pictograph and answer the following questions :
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
(c) How many girls are there in Class VII?
Solution:

Question 3.
In a village, the following pictograph shows the number of fruit baskets sold by six merchants in a particular season:

Observe the above pictograph and answer the following questions:
(i) Which merchant sold the maximum number of baskets?
(ii) How many baskets were sold by Rajinder Singh?
(iii) The merchants who have sold 700 or the number of baskets are planning to buy a cold store for the next season. Can you name them?
Solution:

Question 4.
In Gurgaon, the number of cars sold during a particular week was as follows:

Prepare a pictograph of the cars sold using a symbol of car representing 10 cars and answer the following questions:
(i) On which day the maximum number of cars were sold?
(ii) How many pictures of cars will represent the number of cars sold on Thursday?
Solution:

Question 5.
Total number of animals in five villages are as follows:

Prepare a pictograph of these animals using one symbol ® to represent 10 animals and answer the following questions:
(i) How many symbols represent animals of village E?
(ii) Which village has the maximum number of animals?
(iii) Which village has more animals: village A or village C?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 15 Data Handling Ex 15.1

ML Aggarwal Class 6 Solutions Chapter 15 Data Handling Ex 15.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 15 Data Handling Ex 15.1

Question 1.
Following is the choice of 20 students of class VI of a school:
Banana, Apple, Guava, Orange, Apple, Banana, Orange, Guava, Banana, Banana, Apple, Banana, Apple, Banana, Orange, Guava, Apple, Banana, Guava, Banana.
(i) Arrange the name of fruits in a table using tally marks.
(ii) Which fruit is liked by the maximum number of students?
(iii) Which fruit is liked by the minimum number of students?
Solution:

Question 2.
In a ready-made garment shop, on a particular day the following sizes of shirts were sold:
34, 38, 42, 40, 44, 32, 34, 36, 42, 40, 44, 36, 38, 42, 44, 40, 38, 40, 42, 32, 34, 38, 42, 40, 36, 42, 40, 38, 36, 40.
Arrange the above data in ascending order and construct a frequency distribution table. Also, answer the following questions:
(i) Which shirt size had the maximum sale?
(ii) Which shirt size had the minimum sale?
(iii) The number of shirts sold of size 42 or greater than size 42.
Solution:

Question 3.
In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.

(i) Construct a frequency distribution table for the above data.
(ii) Find how many students obtained 7 marks or more than 7 marks.
(iii) How many students obtained marks below 4?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Check Your Progress

ML Aggarwal Class 6 Solutions Chapter 14 Mensuration Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Check Your Progress

Question 1.
Look at the given figure and fill in the following blanks:

(i) The contribution in the estimation of the given area due to completely covered squares is
(ii) The contribution in the estimation of the given area due to more than half covered squares is
(iii) The contribution in the estimation of the given area due to the exactly half-covered square is
(iv) The contribution in the estimation of the given area due to less than half covered squares is
(v) The total estimated area is
Solution:

Question 2.
The perimeter of a square ABCD is twice the perimeter of ∆PQR. Find the area of the square ABCD.

Solution:

Question 3.
A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle and by how much?
Solution:

Question 4.
A rectangular room is 9 m long and 6 m wide. Find the cost of covering the floor with carpet 2 m wide at ₹35 per metre.
Solution:

Question 5.
If the cost of fencing a square plot at the rate of ₹ 2.50 per metre is ₹ 200, then find the length of each side of the field.
Solution:

Question 6.
If the cost of fencing a rectangular park at the rate of ₹7.50 per metre is ₹600 and the length of the park is 24 m, find the breadth of the park.
Solution:

Question 7.
By splitting the following figures into a rectangle, find their areas (The measures are given in centimetres).

Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Objective Type Questions

ML Aggarwal Class 6 Solutions Chapter 14 Mensuration Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The perimeter of a closed plane figure is the length of its ……….
(ii) The unit of measurement of the perimeter is the same as that of ……….
(iii) If the side of a rhombus is 7 cm then its perimeter is ……….
(iv) The area of a closed plane figure is measured in ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) A centimetre is the unit of area.
(ii) The sum of lengths of a polygon is called its area.
(iii) If the sides of a rectangle are given in centimetres, then its perimeter is measured in square centimetres.
(iv) If the side of a square is doubled, then its perimeter is also doubled.
(v) If the side of a square is doubled, then its area is also doubled.
(vi) To find the cost of constructing a road, we find its area.
(vii) To find the cost of fencing a field, we find its perimeter.
Solution:

Multiple Choice Questions
Choose the correct answer from, the given four options (3 to 15):
Question 3.
If the perimeter of a square is 50 cm, then its side is
(a) 200 cm
(b) 150 cm
(c) 25 cm
(d) 12.5 cm
Solution:

Question 4.
The area of the rectangle with length 25 cm and breadth 12 cm is
(a) 300 sq. m
(b) 74 cm
(c) 300 sq. cm
(d) 74 sq. cm
Solution:

Question 5.
If the perimeter of a square is 36 cm, then its area is
(a) 6 sq. cm
(b) 9 sq. cm
(c) 18 sq. cm
(d) 81 sq. cm
Solution:

Question 6.
If the area of a rectangular plot is 180 sq. m and its length is 15 m, then its breadth is
(a) 12 m
(b) 12 cm
(c) 60 m
(d) 9 m
Solution:

Question 7.
If the length and the breadth of a rectangle are doubled, then its perimeter
(a) remains the same
(b) doubles
(c) becomes four times
(d) becomes half
Solution:

Question 8.
If the length and the breadth of a rectangular are doubled then its area
(a) remains the same
(b) becomes half
(c) doubles
(d) becomes four times.
Solution:

Question 9.
If the sides of a square are halved, then its area
(a) remains the same
(b) becomes half
(c) becomes one-fourth
(d) doubles
Solution:

Question 10.
A square-shaped park ABCD of side 100 m has two equal flower beds of size 10 m x 5 m as shown in the given figure. The perimeter of the remaining park is

(a) 340 m
(b) 370 m
(c) 400 m
(d) 430 m
Solution:

Question 11.
In the given figure, a square of side 1 cm is joined to a square of side 3 cm. The perimeter of the new figure is

(a) 13 cm
(b) 14 cm
(c) 15 cm
(d) 16 cm
Solution:

Question 12.
Two regular hexagons of perimeter 30 cm each are joined as shown in the given figure. The perimeter of the new figure is

(a) 65 cm
(b) 60 cm
(c) 55 cm
(d) 50 cm
Solution:

Question 13.
If the area of a square is numerically equal to its perimeter, then the length of each side is
(a) 1 unit
(b) 2 units
(c) 3 units
(d) 4 units
Solution:

Question 14.
If a ribbon of length 10 m is stitched around a rectangular table cloth making 2 rounds along its boundary, then the perimeter of the table cloth is
(a) 20 m
(b) 10 m
(c) 5 m
(d) 2.5 m
Solution:

Question 15.
A picture is 60 cm wide and 1.8 m long. The ratio of its width to its perimeter in lowest form is
(a) 1 : 2
(b) 1 : 3
(c) 1:6
(d) 1 : 8
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
How many envelopes of size 25 cm x 15 cm can be made from a rectangular sheet of size 4 m x 1.2 m?
Solution:

Question 2.
The perimeter of a rectangle is 36 cm. What will be length and breadth (in natural number) of that rectangle whose area is
(i) maximum?
(ii) minimum?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Ex 14.2

ML Aggarwal Class 6 Solutions Chapter 14 Mensuration Ex 14.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Ex 14.2

Question 1.
Find the area of the region enclosed by the following figures by counting squares:

Solution:

Question 2.
Find the area of the following closed figures by counting squares:

Solution:

Question 3.
Find the areas of the rectangles whose lengths and breadths are:
(i) 9 m and 6 m
(ii) 17 m and 3 m
(iii) 14 m and 4 m
Which one has the largest area and which one has the smallest area?
Solution:

Question 4.
Find the areas of the rectangles whose two adjacent sides are:
(i) 14 cm and 23 cm
(ii) 3 km and 4 km
(iii) 2 m and 90 cm
Solution:

Question 5.
Find the areas of the squares whose sides are:
(i) 8 cm
(ii) 14 m
(iii) 2 m 50 cm
Solution:

Question 6.
A room is 4 m long and 3 m 25 cm wide. How many square metres of carpet is needed to cover the floor of the room?
Solution:

Question 7.
What is the cost of tiling a rectangular field 500 m long and 200 m wide at the rate of ₹7.5 per hundred square metres?
Solution:

Question 8.
A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.
Solution:

Question 9.
In the given figure, find the area of the path (shown shaded) which is 2 m wide all around.

Solution:

Question 10.
Four square flower beds of side 1 m 50 cm are dug on a rectangular piece of land 8 m long and 6 m 50 cm wide. What is the area of the remaining part of the land?
Solution:

Question 11.
How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to cover a rectangular region whose length and breadth are respectively :
(i) 70 cm and 36 cm
(ii) 144 cm and 1 m.
Solution:

Question 12.
The area of a rectangular plot is 340 sq. m. If its breadth is 17 m, find its length and the perimeter.
Solution:

Question 13.
If the area of a rectangular plot is 144 sq. m and its length is 16 m. Find the breadth of the plot and the cost of fencing it at the rate of ₹ 6 per metre.
Solution:

Question 14.
Split the following shapes into rectangles and find their areas. (The measures are given in centimetres).

Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Ex 14.1

ML Aggarwal Class 6 Solutions Chapter 14 Mensuration Ex 14.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 14 Mensuration Ex 14.1

Question 1.
Find the perimeter of each of the following figures:

Solution:

Question 2.
Find the perimeter of each of the following shapes:
(i) A triangle of sides 3 cm, 4 cm and 6 cm.
(ii) A triangle of sides 7 cm, 5.4 cm and 10.2 cm.
(iii) An equilateral triangle of side 11 cm.
(iv) An isosceles triangle with equal sides 10 cm each and third side 7 cm.
Solution:

Question 3.
The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?
Solution:

Question 4.
Table-Top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?
Solution:

Question 5.
A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?
Solution:

Question 6.
Find the perimeter of a regular hexagon with each side measuring 7.5 m.
Solution:

Question 7.
The lengths of two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is the length of its third side?
Solution:

Question 8.
The perimeter of a regular pentagon is 100 cm. How long is its every side?
Solution:

Question 9.
A piece of string is 30 cm long. What will be the length of each side if the string is used to form:
(a) a square?
(b) an equilateral triangle?
(c) a regular hexagon?
Solution:

Question 10.
Find the cost of fencing a rectangular park of length 225 m and breadth 115 m at the rate of ₹13 per metre.
Solution:

Question 11.
Meera went to a rectangular park 140 m long and 90 m wide. She took 5 complete rounds on its boundary. What is the distance covered by her?
Solution:

Question 12.
Pinky runs 8 times around a rectangular park with length 80 m and breadth 55 m while Pankaj runs 7 times around a square park of side 75 cm. Who covers more distance and by how much?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress

Question 1.
Draw a line segment AB = 5.4 cm. Construct a perpendicular at A by using ruler and compass.
Solution:
Steps of Construction:

Question 2.
Draw a line segment PQ = 6.8 cm. Draw a perpendicular to it from a point A outside PQ by using ruler and compass.
Solution:

Question 3.
Draw a line segment of length 6.5 cm and construct its axis of symmetry.
Solution:

Question 4.
Draw ∠AOB = 76° with the help of a protractor. Bisect this angle by using a ruler and compass. Measure the two parts by your protractor and see how accurate you are.
Solution:
Steps of Construction:

Question 5.
By using and compass, construct an angle of 135° and bisect it. Measure any one part by protractor and see how accurate you are.
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A ruler is used to draw a line and to measure their …………
(ii) A divider is used to compare …………
(iii) A compass is used to draw circles or arcs of …………
(iv) A protractor is used to draw and measure …………
(v) The set squares are two triangular pieces having angles of ………… and …………
(vi) To bisect a line segment of length 7 cm, the opening of the’ compass should be more than …………
(vii) The perpendicular bisector of a line segment is also its line of …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) There is only one set square in a geometry box.
(ii) An angle can be copied with the help of a ruler and compass.
(iii) The perpendicular bisector of a line segment can be drawn by paper folding.
(iv) Perpendicular to a line from a given point not on it can be drawn by paper folding.
(v) A 45° – 45° – 90° set square and a protractor have the same number of line(s) of symmetry.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 13):
Question 3.
A circle of any radius can be constructed with the help of a:
(a) ruler
(b) divider
(c) compass
(d) protractor
Solution:
compass (c)

Question 4.
The instrument in a geometry box having the shape of a semicircle is :
(a) ruler
(b) divider
(c) compass
(d) protractor
Solution:

Question 5.
The instrument to measure an angle is
(a) ruler
(b) protractor.
(c) divider
(d) compass
Solution:
protractor (b)

Question 6.
Which of the following angles cannot be constructed using a ruler and compass?
(a) 15°
(b) 45°
(c) 75°
(d) 85°
Solution:
85° (d)

Question 7.
The number of perpendiculars that can be drawn to a line from a point not on it is
(a) 1
(b) 2
(c) 4
(d) infinitely many
Solution:
1 (a)

Question 8.
The number of perpendicular bisectors that can be drawn of a given line segment is :
(a) 0
(b) 1
(c) 2
(d) infinitely many
Solution:
1 (b)

Question 9.
The number of lines of symmetry in a picture of a divider is The number of lines of symmetry in a picture of a compass is
(a) 0
(b) 1
(c) 2
(d) 4
Solution:
1 (b)

Question 10.
The number of lines of symmetry in a picture of a compass is
(a) 0
(b) 1
(c) 2
(d) none of these
Solution:
0 (a)

Question 11.
The number of lines of symmetry in a ruler is
(a) 0
(b) 1
(c) 2
(d) 4
Solution:
2 (c)

Question 12.
The number of lines of symmetry in a 30° – 60° – 90° set square is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:
0 (a)

Question 13.
The number of lines of symmetry in a protractor is
(a) 0
(b) 1
(c) 2
(d) more than 2
Solution:
1 (b)

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Ex 13.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3

Question 1.
Draw an angle of 80° and make a copy of it using ruler and compass.
Solution:

Question 2.
Draw an angle of measure 127° and construct its bisector.
Solution:

Question 3.
Draw ∠POQ = 64°. Also, draw its line of symmetry.
Solution:

Question 4.
Draw a right angle and construct its bisector.
Solution:

Question 5.
Draw an angle of 152° and divide it into four equal parts.
Solution:

Question 6.
Draw an angle of measure 45° and bisect it.
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Ex 13.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2

Question 1.
Draw a line segment $$\overline{\mathrm{PQ}}$$ =5.6 cm. Draw a perpendicular to it from a point A outside $$\overline{\mathrm{PQ}}$$ by using ruler and compass.
Solution:

Question 2.
Draw a line segment $$\overline{\mathrm{AB}}$$ = 6.2 cm. Draw a perpendicular to it at a point M on $$\overline{\mathrm{AB}}$$ by using ruler and compass.
Solution:

Question 3.
Draw a line l and take a point P on it. Through P, draw a line segment $$\overline{\mathrm{PQ}}$$ perpendicular to l. Now draw a perpendicular to $$\overline{\mathrm{PQ}}$$ at Q (use ruler and compass).
Solution:

Question 4.
Draw a line segment $$\overline{\mathrm{AB}}$$ of length 6.4 cm and construct its axis of symmetry (use ruler and compass).
Solution:

Question 5.
Draw the perpendicular bisector of $$\overline{\mathrm{XY}}$$ whose length is 8.3 cm.
(i) Take any point P on the bisector drawn. Examine whether PX = PY.
(ii) If M is the mid-point of $$\overline{\mathrm{XY}}$$, what can you say about the lengths MX and MY?
Solution:

Question 6.
Draw a line segment of length 8.8 cm. Using ruler and compass, divide it into four equal parts. Verify by actual measurement.
Solution:

Question 7.
With $$\overline{\mathrm{PQ}}$$ of length 5.6 cm as diameter, draw a circle.
Solution:

Question 8.
Draw a circle with centre C and radius 4.2 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.
Solution:

Question 9.
Draw a circle of radius 3.5 cm. Draw any two of its (non-parallel) chords. Construct the perpendicular bisectors of these chords. Where do they meet?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Ex 13.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1

Question 1.
(i) 2 cm
(ii) 3.5 cm
Solution:

Question 2.
With the same centre O, draw two circles of radii 2.6 cm and 4.1 cm.
Solution:

Question 3.
Draw any circle and mark points A, B and C such that
(i) A is on the circle.
(ii) B is in the interior of the circle.
(iii) C is in the exterior of the circle.
Solution:

Question 4.
Draw a circle and any two of its (non-perpendicular) diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?
Solution:

Question 5.
Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D.
Examine whether $$\overline{\mathrm{AB}}$$ and $$\overline{\mathrm{CD}}$$ are at right angles.
Solution:

Question 6.
Construct a line segment of the length of 6.3 cm using ruler and compass.
Solution:

Question 7.
Construct $$\overline{\mathrm{AB}}$$ of length 8.3 cm. From this cut off $$\overline{\mathrm{AC}}$$ of length 5.6 cm. Measure the length of BC . .
Solution:

Question 8.
Draw any line segment $$\overline{\mathrm{PQ}}$$. Without measure $$\overline{\mathrm{PQ}}$$, construct a copy of $$\overline{\mathrm{PQ}}$$.
Solution:

Question 9.
Given some line segment $$\overline{\mathrm{AB}}$$, whose length you do not know, construct $$\overline{\mathrm{PQ}}$$ such that the length of $$\overline{\mathrm{PQ}}$$ is twice that of $$\overline{\mathrm{AB}}$$.
Solution:

Question 10.
Take a line segment $$\overline{\mathrm{PQ}}$$ of length 10 cm. From $$\overline{\mathrm{PQ}}$$, cut of $$\overline{\mathrm{PA}}$$ of length 4.3 cm and $$\overline{\mathrm{BQ}}$$ of length 2.5 cm. Measure the length of segment $$\overline{\mathrm{AB}}$$.
Solution:

Question 11.
Given two line segments $$\overline{\mathrm{AB}}$$ and $$\overline{\mathrm{CD}}$$ of length 7.5 cm and 4.6 respectively. Construct line segments.
(i) $$\overrightarrow { PQ }$$ of length equal to the sum of the lengths of $$\overline{\mathrm{AB}}$$ and $$\overline{\mathrm{CD}}$$.
(ii) $$\overline{\mathrm{XY}}$$ of length equal to the difference of the lengths of $$\overline{\mathrm{AB}}$$ and $$\overline{\mathrm{CD}}$$. Verify these lengths by measurements.
Solution: