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Page 1 When we talk about some plane figures as shown below we think of their regions and their boundaries. We need some measures to compare them. We look into these now. 10.2 Perimeter Look at the following figures (Fig. 10.1). Y ou can make them with a wire or a string. If you start from the point S in each case and move along the line segments then you again reach the point S. You have made a complete round of the 10.1 Introduction Chapter 10 Chapter 10 Chapter 10 Chapter 10 Chapter 10 Mensuration Mensuration Mensuration Mensuration Mensuration Rationalised 202324 Page 2 When we talk about some plane figures as shown below we think of their regions and their boundaries. We need some measures to compare them. We look into these now. 10.2 Perimeter Look at the following figures (Fig. 10.1). Y ou can make them with a wire or a string. If you start from the point S in each case and move along the line segments then you again reach the point S. You have made a complete round of the 10.1 Introduction Chapter 10 Chapter 10 Chapter 10 Chapter 10 Chapter 10 Mensuration Mensuration Mensuration Mensuration Mensuration Rationalised 202324 MATHEMATICS 154 shape in each case (a), (b) & (c). The distance covered is equal to the length of wire used to draw the figure. This distance is known as the perimeter of the closed figure. It is the length of the wire needed to form the figures. The idea of perimeter is widely used in our daily life. l A farmer who wants to fence his field. l An engineer who plans to build a compound wall on all sides of a house. l A person preparing a track to conduct sports. All these people use the idea of ‘perimeter’. Give five examples of situations where you need to know the perimeter. Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once. 1. Measure and write the length of the four sides of the top of your study table. AB = ____ cm BC = ____ cm CD = ____ cm DA = ____ cm Now, the sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter? 2. Measure and write the lengths of the four sides of a page of your notebook. The sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter of the page? 3. Meera went to a park 150 m long and 80 m wide. She took one complete round on its boundary. What is the distance covered by her? Rationalised 202324 Page 3 When we talk about some plane figures as shown below we think of their regions and their boundaries. We need some measures to compare them. We look into these now. 10.2 Perimeter Look at the following figures (Fig. 10.1). Y ou can make them with a wire or a string. If you start from the point S in each case and move along the line segments then you again reach the point S. You have made a complete round of the 10.1 Introduction Chapter 10 Chapter 10 Chapter 10 Chapter 10 Chapter 10 Mensuration Mensuration Mensuration Mensuration Mensuration Rationalised 202324 MATHEMATICS 154 shape in each case (a), (b) & (c). The distance covered is equal to the length of wire used to draw the figure. This distance is known as the perimeter of the closed figure. It is the length of the wire needed to form the figures. The idea of perimeter is widely used in our daily life. l A farmer who wants to fence his field. l An engineer who plans to build a compound wall on all sides of a house. l A person preparing a track to conduct sports. All these people use the idea of ‘perimeter’. Give five examples of situations where you need to know the perimeter. Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once. 1. Measure and write the length of the four sides of the top of your study table. AB = ____ cm BC = ____ cm CD = ____ cm DA = ____ cm Now, the sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter? 2. Measure and write the lengths of the four sides of a page of your notebook. The sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter of the page? 3. Meera went to a park 150 m long and 80 m wide. She took one complete round on its boundary. What is the distance covered by her? Rationalised 202324 MENSURATION 155 4. Find the perimeter of the following figures: (a) (b) (c) (d) So, how will you find the perimeter of any closed figure made up entirely of line segments? Simply find the sum of the lengths of all the sides (which are line segments). Perimeter = AB + BC + CD + DA = __+__+__+__ = ______ Perimeter = AB + BC + CD + DA = __ + __ + __+ __ = ______ Perimeter = AB + BC + CD + DE + EF + FG + GH +HI + IJ + JK + KL + LA = __ + __ +__ + __ + __ + __ + __ + __ +__+ __ + __ + __ = ______ Perimeter = AB + BC + CD + DE + EF + FA = __ + __ + __ + __ + __ + __ = ______ Rationalised 202324 Page 4 When we talk about some plane figures as shown below we think of their regions and their boundaries. We need some measures to compare them. We look into these now. 10.2 Perimeter Look at the following figures (Fig. 10.1). Y ou can make them with a wire or a string. If you start from the point S in each case and move along the line segments then you again reach the point S. You have made a complete round of the 10.1 Introduction Chapter 10 Chapter 10 Chapter 10 Chapter 10 Chapter 10 Mensuration Mensuration Mensuration Mensuration Mensuration Rationalised 202324 MATHEMATICS 154 shape in each case (a), (b) & (c). The distance covered is equal to the length of wire used to draw the figure. This distance is known as the perimeter of the closed figure. It is the length of the wire needed to form the figures. The idea of perimeter is widely used in our daily life. l A farmer who wants to fence his field. l An engineer who plans to build a compound wall on all sides of a house. l A person preparing a track to conduct sports. All these people use the idea of ‘perimeter’. Give five examples of situations where you need to know the perimeter. Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once. 1. Measure and write the length of the four sides of the top of your study table. AB = ____ cm BC = ____ cm CD = ____ cm DA = ____ cm Now, the sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter? 2. Measure and write the lengths of the four sides of a page of your notebook. The sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter of the page? 3. Meera went to a park 150 m long and 80 m wide. She took one complete round on its boundary. What is the distance covered by her? Rationalised 202324 MENSURATION 155 4. Find the perimeter of the following figures: (a) (b) (c) (d) So, how will you find the perimeter of any closed figure made up entirely of line segments? Simply find the sum of the lengths of all the sides (which are line segments). Perimeter = AB + BC + CD + DA = __+__+__+__ = ______ Perimeter = AB + BC + CD + DA = __ + __ + __+ __ = ______ Perimeter = AB + BC + CD + DE + EF + FG + GH +HI + IJ + JK + KL + LA = __ + __ +__ + __ + __ + __ + __ + __ +__+ __ + __ + __ = ______ Perimeter = AB + BC + CD + DE + EF + FA = __ + __ + __ + __ + __ + __ = ______ Rationalised 202324 MATHEMATICS 156 Fig 10.3 Find the perimeter of the following rectangles: Length of Breadth of Perimeter by adding Perimeter by rectangle rectangle all the sides 2 × (Length + Breadth) 25 cm 12 cm = 25 cm + 12 cm = 2 ×(25 cm + 12 cm) + 25 cm + 12 cm = 2 × (37 cm) = 74 cm = 74 cm 0.5 m 0.25 m 18 cm 15 cm 10.5 cm 8.5 cm 10.2.1 Perimeter of a rectangle Let us consider a rectangle ABCD (Fig 10.2) whose length and breadth are 15 cm and 9 cm respectively. What will be its perimeter? Perimeter of the rectangle = Sum of the lengths of its four sides. = AB + BC + CD + DA = AB + BC + AB + BC = 2 × AB + 2 × BC = 2 × (AB + BC) = 2 × (15cm + 9cm) = 2 × (24cm) = 48 cm Hence, from the said example, we notice that Perimeter of a rectangle = length + breadth + length + breadth i.e. Perimeter of a rectangle = 2 × (length + breadth) Let us now see practical applications of this idea : Example 1 : Shabana wants to put a lace border all around a rectangular table cover (Fig 10.3), 3 m long and 2 m wide. Find the length of the lace required by Shabana. Solution : Length of the rectangular table cover = 3 m Breadth of the rectangular table cover = 2 m Shabana wants to put a lace border all around the table cover. Therefore, the length of the lace required will be equal to the perimeter of the rectangular table cover. Remember that opposite sides of a rectangle are equal so AB = CD, AD = BC Fig 10.2 Rationalised 202324 Page 5 When we talk about some plane figures as shown below we think of their regions and their boundaries. We need some measures to compare them. We look into these now. 10.2 Perimeter Look at the following figures (Fig. 10.1). Y ou can make them with a wire or a string. If you start from the point S in each case and move along the line segments then you again reach the point S. You have made a complete round of the 10.1 Introduction Chapter 10 Chapter 10 Chapter 10 Chapter 10 Chapter 10 Mensuration Mensuration Mensuration Mensuration Mensuration Rationalised 202324 MATHEMATICS 154 shape in each case (a), (b) & (c). The distance covered is equal to the length of wire used to draw the figure. This distance is known as the perimeter of the closed figure. It is the length of the wire needed to form the figures. The idea of perimeter is widely used in our daily life. l A farmer who wants to fence his field. l An engineer who plans to build a compound wall on all sides of a house. l A person preparing a track to conduct sports. All these people use the idea of ‘perimeter’. Give five examples of situations where you need to know the perimeter. Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once. 1. Measure and write the length of the four sides of the top of your study table. AB = ____ cm BC = ____ cm CD = ____ cm DA = ____ cm Now, the sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter? 2. Measure and write the lengths of the four sides of a page of your notebook. The sum of the lengths of the four sides = AB + BC + CD + DA = ___ cm +___ cm +___ cm +___ cm = _____ cm What is the perimeter of the page? 3. Meera went to a park 150 m long and 80 m wide. She took one complete round on its boundary. What is the distance covered by her? Rationalised 202324 MENSURATION 155 4. Find the perimeter of the following figures: (a) (b) (c) (d) So, how will you find the perimeter of any closed figure made up entirely of line segments? Simply find the sum of the lengths of all the sides (which are line segments). Perimeter = AB + BC + CD + DA = __+__+__+__ = ______ Perimeter = AB + BC + CD + DA = __ + __ + __+ __ = ______ Perimeter = AB + BC + CD + DE + EF + FG + GH +HI + IJ + JK + KL + LA = __ + __ +__ + __ + __ + __ + __ + __ +__+ __ + __ + __ = ______ Perimeter = AB + BC + CD + DE + EF + FA = __ + __ + __ + __ + __ + __ = ______ Rationalised 202324 MATHEMATICS 156 Fig 10.3 Find the perimeter of the following rectangles: Length of Breadth of Perimeter by adding Perimeter by rectangle rectangle all the sides 2 × (Length + Breadth) 25 cm 12 cm = 25 cm + 12 cm = 2 ×(25 cm + 12 cm) + 25 cm + 12 cm = 2 × (37 cm) = 74 cm = 74 cm 0.5 m 0.25 m 18 cm 15 cm 10.5 cm 8.5 cm 10.2.1 Perimeter of a rectangle Let us consider a rectangle ABCD (Fig 10.2) whose length and breadth are 15 cm and 9 cm respectively. What will be its perimeter? Perimeter of the rectangle = Sum of the lengths of its four sides. = AB + BC + CD + DA = AB + BC + AB + BC = 2 × AB + 2 × BC = 2 × (AB + BC) = 2 × (15cm + 9cm) = 2 × (24cm) = 48 cm Hence, from the said example, we notice that Perimeter of a rectangle = length + breadth + length + breadth i.e. Perimeter of a rectangle = 2 × (length + breadth) Let us now see practical applications of this idea : Example 1 : Shabana wants to put a lace border all around a rectangular table cover (Fig 10.3), 3 m long and 2 m wide. Find the length of the lace required by Shabana. Solution : Length of the rectangular table cover = 3 m Breadth of the rectangular table cover = 2 m Shabana wants to put a lace border all around the table cover. Therefore, the length of the lace required will be equal to the perimeter of the rectangular table cover. Remember that opposite sides of a rectangle are equal so AB = CD, AD = BC Fig 10.2 Rationalised 202324 MENSURATION 157 Now, perimeter of the rectangular table cover = 2 × (length + breadth) = 2 × (3 m + 2 m) = 2 × 5 m = 10 m So, length of the lace required is 10 m. Example 2 : An athlete takes 10 rounds of a rectangular park, 50 m long and 25 m wide. Find the total distance covered by him. Solution : Length of the rectangular park = 50 m Breadth of the rectangular park = 25 m Total distance covered by the athlete in one round will be the perimeter of the park. Now, perimeter of the rectangular park = 2 × (length + breadth)= 2 × (50 m + 25 m) = 2 × 75 m = 150 m So, the distance covered by the athlete in one round is 150 m. Therefore, distance covered in 10 rounds = 10 × 150 m = 1500m The total distance covered by the athlete is 1500 m. Example 3 : Find the perimeter of a rectangle whose length and breadth are 150 cm and 1 m respectively. Solution : Length = 150 cm Breadth = 1m = 100 cm Perimeter of the rectangle = 2 × (length + breadth) = 2 × (150 cm + 100 cm) = 2 × (250 cm) = 500 cm = 5 m Example 4 : A farmer has a rectangular field of length and breadth 240 m and 180 m respectively. He wants to fence it with 3 rounds of rope as shown in figure 10.4. What is the total length of rope he must use? Solution : The farmer has to cover three times the perimeter of that field. Therefore, total length of rope required is thrice its perimeter. Perimeter of the field = 2 × (length + breadth) = 2 × ( 240 m + 180 m) = 2 × 420 m = 840 m Total length of rope required = 3 × 840 m = 2520 m 150 cm 150 cm 1 m 1 m Fig 10.4 Rationalised 202324Read More
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