202110795-TRAVELLER_PREMIUM-STUDENT-TEXTBOOK-MATHEMATICS-G05-PART2

1 × 1 cm 2 = ×b sq. units. 1 cm Observe the triangle formed from a square. 1 The area of the triangle = 2 of the area of the square 1 = 2 ×s×s Area of triangle = 1 × base × height Since, we cannot use two different formulae 2 for the area of a triangle; we give one common formula as 1 Area of a triangle = 2 × base (length or side) × height (breadth or side) 1 = 2 × b × h sq. units Example 8: Find the areas of the given triangles: a) b) c) 9 cm 9 cm 10 cm 6 cm 8.5 cm 9.8 cm Solution: 1 a) Area of a triangle = × b × h sq. units 2 = 1 × 8.5 cm × 9 cm = 38.25 sq. cm 2 b) Area of a triangle = 1 × b × h sq. units 2 1 = 2 × 9.8 cm × 10 cm = 49 sq. cm c) Area of a triangle = 1 × b × h sq. units 2 1 = 2 × 6 cm × 9 cm = 27 sq. cm Measurement 97

? Train My Brain Find the perimeters of the given figures. a) 4 cm 2 cm b) 6 cm 6.5 cm 5 cm c) 6 cm 3 cm 2 cm 4.5 cm 5 cm 3 cm 2.5 cm I Apply Let us see a few examples where we can apply the concepts of perimeter and area. Example 9: Find the areas of the given figures. 2 cm 1 cm a) 2 cm b) c) 2 cm 7 cm 4 cm 7 cm 6 cm 3 cm 4 cm 4 cm 5 cm 3 cm Solution: a) Area of the given figure = Area of triangle + Area of rectangle = [( 1 × 3 × 2)+ (3 × 7)] sq. cm 2 = (3 + 21) sq. cm = 24 sq. cm b) Area of the given figure = Area of square + Area of rectangle = [(4 × 4) + (2 × 7)] sq. cm = (16 + 14) sq. cm = 30 sq. cm c) Area of the given figure = Area of rectangle 1 +Area of rectangle 2 + Area of rectangle 3 = [(1 × 6) + (3 × 4) + (2 × 5)] sq. cm = (6 + 12 + 10) sq. cm = 28 sq. cm 98

Example 10: Adil made a park on the two sides of his house as shown. The length of his2m 2m house is 15 m and its breadth is 10 m. The breadth of the park is 2 m. Find the area of the park. park Adil’s house 10 m 15 m 2m Solution: Adil’s park can be divided into two different rectangles. We know the breadth of the park = 2 m Therefore, length of rectangle 1 = 15 m + 2 m = 17 m Length of rectangle 2 = 10 m 17 m 1 park 2 Adil’s house 10 m 15 m 2m Area of rectangle 1 =  × b = 17 m × 2 m = 34 sq. m. Area of rectangle 2 =  × b = 10 m × 2 m = 20 sq. m. Therefore, the total area of the park = 34 sq.m. + 20 sq.m. = 54 sq. m. Measurement 99

I Explore (H.O.T.S.) Let us see some more examples of perimeter and area. Example 11: Complete the table given for different rectangles. One has been done for you. Length Breadth Perimeter Area a) 7 cm 5 cm 24 cm 35 sq cm b) 10 cm 8 cm c) 11 cm 44 cm d) 6 cm 60 sq. cm Solution: a) Length = 7 cm Given perimeter = 2 × ℓ + 2 × b = 24 cm So, 2 × 7 cm + 2 × b = 24 cm. 14 + 2 × b = 24 cm So, 10 should be added to 14 to get 24. 2 × b = 10 cm Therefore, b = 5 cm Area = ℓ × b = 7 × 5 = 35 cm Example 12: An assembly hall is 16 m long and 12 m wide. If the cost of laying 1 sq. m is ` 50, what would be the labour cost for laying the floor of the assembly hall? Solution: The area of the assembly hall = b × h = (16 × 12) sq. m. = 192 sq. m. Cost of laying 1 sq. m. = ` 50 Cost of laying 192 sq. m. = ` 50 × 192 = ` 9600 Therefore, the labour cost for laying the floor of the assembly hall is ` 9600. Maths Munchies π The number ‘π’ is used to find the perimeter, area and volume of circular figures. The value of π is 22 . 7 100

Connect the Dots Social Studies Fun India’s area spans about 3.287 million km2. It is the 7th largest country in the world. Science Fun Do you know one-ninth volume of ice floats above water because it is about 9% less heavier than liquid water. So, a litre of ice weighs less than a litre of water. Drill Time 14.1 Conversion of Units of Measurement 1) Convert the following: a) 1350 mg into g b) 2 kℓ 810 ℓ into kℓ c) 4 m 20 cm into cm d) 75.32 km into m e) 4.318 kg into kg and g f) 584 cm into mm 2) Compare the below measures using <, > or =. a) 4.8 kg ______ 4800 g b) 13 ℓ ______ 13901 mℓ c) 84771 m ______ 84.77 km d) 1580 ℓ ______ 1.6 kℓ Measurement 101

3) Solve the following: a) Add 35.673 ℓ and 72.145 ℓ. b) Subtract 44.352 m from 51.401 m. c) Multiply 138 g by 23. d) Divide 192 cm by 4. 14.2 Area and Perimeter 4) Find the perimeter of the following: a) A square of side 12 cm. b) A rectangle with  = 15 cm and b = 3.5 cm. c) 2.5 cm 3.5 cm 4 cm 5 cm 5.8 cm d) 4 cm 6.3 cm 5.5 cm 5) Find the areas of the given figures. a) 6 cm 3 cm 4 cm 7 cm 2 cm 4 cm 102

b) 4 cm 3 cm 5.3 cm c) 5 cm 5 cm 5 cm 5 cm 3.6 cm 1.2 cm A Note to Parent Give your child some matchsticks and tell them that each matchstick is of 5 cm. Then, ask your child to make different shapes such as triangle, square and rectangle and to find their respective perimeters. Measurement 103

Chapter Data Handling 15 I Will Learn About • interpreting pie charts and line graphs. 15.1 Line Graphs and Pie Charts I Think Pooja was reading a Science lesson from her sister’s book. She saw a chart showing the distribution of gases in the air as shown. She did not understand what it was and how to read it. She asked her sister about it. Do you understand such charts? I Recall Let us recall the concept of the bar graph that we have already learnt in Grade 4. Look at the given bar graph. The sale of TV sets for different months in a shop is given in the graph. Study the graph and answer the questions that follow. 104

Y-axis Sale of TV sets Number of TVs 30 25 20 15 10 5 Feb. Apr. Jun. Aug. Oct. X-axis Months a) How many TV sets were sold in June? b) In which month were 10 TV sets sold? c) In which month was the maximum number of TV sets sold? d) How many TV sets were sold in February? e) In which month was the minimum number of TV sets sold? I Remember and Understand In class IV, we have learnt about bar graphs in detail. Now, let us learn another type of representation of data, called the circle graph. Circle graph: A circle divided into parts to show the fraction of Circle graphs are each category of data is called a circle graph or circle chart. also called pie charts. Let us understand this through some examples. Example 1: The students of class V spent a week at a summer camp. At the end of the week, the students were asked about their favourite activity in the camp. The given circle graph shows their responses. Study the graph and answer the questions that follow. Data Handling 105

Riding a Horse Favourite Activity of Students Art and Craft Class Dancing Playing Cricket a) W hich activity did the students enjoy the most? b) Of the two classes, Dancing and Art & Craft classes, which one was more preferred by the students? c) W hat fraction of the students chose horse riding as their favourite activity? d) Which activity did the students enjoy the least? e) W hat fraction of the students chose cricket as their favourite activity? Solution: a) The students enjoyed horse riding the most. b) Dancing class was more preferred by the students. c) Half of the students chose horse riding as their favourite activity. d) The students enjoyed Art & Craft the least. e) One-fourth of students chose cricket as their favourite activity. Example 2: The time spent by Arun for completing his homework is given as a circle graph. Observe the graph and answer the questions that follow. Spelling - 12 % Time Spent on Homework Reading - 8 % Social Studies - 15 % Maths - 30 % English - 15 % Science 106

a) On which subject did Arun spend the maximum time? b) On which subject did Arun spend the least time? c) On which two subjects did Arun spend the same amount of time? d) What percent of the time was spent on Science? e) What is the total time spent on reading and spelling? Solution: a) Arun spent the maximum time on Maths. b) Arun spent the least time on reading. c) Arun spent the same amount of time on English and Social Studies. d) Percentage of time spent on Science = [100 – (15 + 15 + 30 + 12 + 8)] % = (100 – 80)% = 20% e) The total time spent on reading and spelling is 12% + 8% = 20% We have learnt about pie charts. Now, let us learn about line graphs. Consider the given example. Example 3: Reema recorded the height of a plant from the time it was a month old. Observe the line graph and answer the questions that follow. Y-axis Growth of a Plant Scale: 65 On X-axis: 1 cm = 1 month On Y-axis: 1 cm = 5 cm 60 Height (in cm) 55 50 45 40 1 2 3 4 5 6 7 8 9 10 X-axis Months a) What was the height of the plant when it was 1 month old? b) In which month was the plant 55 cm in height? c) What was the height of the plant when it was 5 months old? Data Handling 107

Solution: a) The height of the plant was 40 cm, when it was 1 month old. b) The height of the plant was 55 cm, when it was four months old. c) The height of the plant was 60 cm, when it was 5 months old. ? Train My Brain Rainfall in August T he amount of rainfall in August is given in the Week 2 Week 1 circle graph. Observe the graph and answer the 17 % questions. 25 % a) W hich week had the maximum rainfall? Week 3 Week 4 40 % 18 % b) Which week had the least rainfall? c) What was the total rainfall in the second and the fourth weeks? I Apply Let us look at some real-life situations where we use pie-charts. Example 4: In a class of 48 students, 6 students come to school by car, 18 students come by bus, 12 students come by bicycle and 12 students come by auto. Draw a circle graph according to the data. Solution: Follow these steps to draw a circle graph. Step 1: Represent the data in tabular form. Class Means of transport Number of students Car 6 Bus 18 Bicycle 12 Auto 12 108

Step 2: Determine the fraction or percentage of the given data groups. Step 3: Means of Number of Class Percentage transport students Fraction 1 × 100% = 12.5% 8 Car 6 6 = 1 48 8 Bus 18 18 = 3 3 × 100% = 37.5% Bicycle 12 48 8 8 12 12 = 2 Auto 48 8 2 × 100% = 25% 12 = 2 8 48 8 2 × 100% = 25% 8 Draw a circle and divide it into 8 equal parts. Step 4: From step 2 we can conclude that 1 part out of 8 parts can be coloured for car. Similarly, 3, 2 and 2 parts out of 8 can be coloured for bus, bicycle and auto respectively. Auto Means of Transport of Students 25 % Car 12.5 % Bicycle Bus 25 % 37.5 % Data Handling 109

Example 5: The number of seeds planted by Ram in a week is given in the table. Draw a line graph. Days of the week Number of seeds planted Sunday 1 Monday 1 Tuesday 2 3 Wednesday 4 Thursday 5 Friday 5 Saturday Solution: Follow the steps to draw the line graph. Step 1: Draw a graph with the days of the week on the X-axis and the number of seeds planted on Y-axis as shown. Y-axis Number of seeds planted 6 5 4 3 2 1 Sun. Mon. Tue. Wed. Thu. Fri. Sat. X-axis Days of the week Step 2: Place dots where the data of the X-axis and the Y-axis intersect as given in the table. 110

Y-axis Number of seeds planted 6 5 4 3 2 1 Sun. Mon. Tue. Wed. Thu. Fri. Sat. X-axis Days of the week Step 3: Draw a line joining the dots to make the line graph. Give suitable title Y-axis and scale. Number of seeds planted 6 5 4 3 2 1 Sun. Mon. Tue. Wed. Thu. Fri. Sat. X-axis Days of the week Data Handling 111

I Explore (H.O.T.S.) Let us draw a few more circle graphs for the data given. Example 6: The marks obtained in a test by the students of Class V are given. Prepare the tally marks, draw a circle graph for the same and answer the questions that follow. 34, 32, 32, 30, 30, 30, 32, 34, 32, 30, 34, 30, 32, 34, 30, 30, 43, 43, 34, 32, 32, 30, 34, 34, 32, 30, 30, 43, 34, 30, 34, 32, 30, 43, 30, 43, 30, 34, 30, 32 a) Which mark is obtained by most of the students? b) Which mark is obtained by the least number of students? c) How many students obtained the highest mark? d) How many students obtained the least mark? e) What percent of students obtained 30 marks? f) How many students are there in the class? Solution: Marks of Class V students Marks Tally marks Number of Fraction 30 Students 32 15 = 3 34 15 40 8 43 10 = 2 10 40 8 10 = 2 10 40 8 5 =1 5 40 8 112

Performance of Class V students 32 marks 10 students 30 marks 15 students 43 marks 34 marks 5 students 10 students a) 30 marks b) 43 marks c) 5 students d) 15 students e) 1450 ×100% = 37.5% f) 40 students Example 7: The different aspirations of the students of a class are as given: Doctor, Engineer, Scientist, Doctor, Businessman, Engineer, Doctor, Engineer, Engineer, CA, Businessman, Businessman, Doctor, Engineer, Scientist, Doctor, Engineer, Engineer, Scientist, Doctor, Engineer, Scientist, Businessman, Engineer, Scientist, Engineer, Doctor, Engineer, Scnientist, CA, Engineer, Doctor Draw a circle graph from the tally marks table and answer these questions: a) Which profession do most students want to follow? b) W hich profession do the least number of students want to follow? c) How many students want to become businessmen? d) H ow many students want to become scientists? e) How many students are there in the class altogether? Data Handling 113

Solution: Aspiration of students of a class Profession Tally marks Number of Fraction of students students Doctor 8 8 =4 = 25 % 32 16 Engineer 12 12 = 6 = 37.50 % 32 16 Scientist 6 6 = 3 = 18.75 % 32 16 Businessman 4 4 = 2 = 12.50 % 32 16 CA 2 2 =1 = 6.25 % 32 16 We divide a circle into 16 parts and represent these as fractions of the total number of students. Aspiration of students of a class a) Engineer 6.25% b) CA Businessman CA 12.50% c) 4 Scientist Doctor d) 6 18.75% 25% e) 32 Engineer 37.50 Maths Munchies The angle in a pie chart tell us about the data shown. When the angle in the pie chart is 90º it means that the data shown is a quarter of the total. When the angle in the pie chart is 180º, it means that the data shown is half of the total. 114

Connect the Dots Science Fun Healthy Diet A healthy diet should consist of: Heafaltthsy 15% Proteins 25% Proteins 25% Carbohydrates 30% Vegetables 30% Carbo3h0y%drates Vegetables 30% Healthy fats 15% Social Studies Fun In 2017, the estimated population of India was 1.3 billion. This makes India the country with the second highest population after the Republic of China. India’s area is 2.4% of the world’s land surface. 17.5% of the world’s population lives here. Drill Time 15.1 Line Graphs and Pie Charts 1) Solve the following: a) Draw a circle graph based on the following data. Pets owned by people Number of people Dog 6 Cat 2 Fish 2 1 Rabbit 1 Parrot Data Handling 115

b) Raghu spends his day as given. At school 8 hours Playing 2 hours 2 hours Doing Homework 1 hour Reading 3 hours 8 hours Routine work Sleeping Draw a circle graph based on the data given in the table. c) T he data shows the number of students and their favourite games. Draw a line graph based on the data. Favourite game Number of students Football 15 Cricket 20 25 Basketball 20 Volleyball 20 Kabaddi A Note to Parent Ask your child to count the number of glasses of water he or she drinks in a week. Categorise them in days using a table of tally marks. Then draw a circle graph for the same. Create other such opportunities for your child to practise data handing. 116