NCERT Class 7 Maths Chapter 11 Perimeter and Area Exercise 11.1

Chapter 11 Perimeter and Area Exercise 11.1

Question 1: The length and the breadth of a rectangular piece of land are 500 m and 300 m, respectively. Find:
(i) Its area
(ii) The cost of the land, if 1 m2 of the land costs ₹ 10,000.
Answer:

Given
Length of rectangular land = 500 m
Breadth of rectangular land = 300 m
To find = Area
               Cost of land

(i) Area of rectangle = l x b
                 = 500 x 300
                 = 150000 m²
Therefore, the area of the rectangular land is 150000 m².

(ii) Area of rectangular land = 150000 m²
Cost of 1 m² land = ₹ 10000
Cost of 150000 m² land = ?
= 10000 x 150000
= ₹ 1,50,00,00,000
Therefore, the cost of the land is ₹ 1,50,00,00,000.

Question 2: Find the area of a square park whose perimeter is 320 m.
Answer:
Given
Perimeter of a square park = 320 m
To find - Side length
       Area
Side = perimeter/4
        = 320/4
        = 80 m
Therefore, the length of each side is 80 m.
Area of Square = side x side
         = 80 x 80
        = 6400 m²
Therefore, the area of square park is 6400 m².

Question 3: Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also find its perimeter.
Answer:
Given
Area of rectangular plot = 440 m²
Length of rectangular plot = 22 m
To find - Breadth
       Perimeter
Breadth = Area/Length
  = 440/22
  = 20 m
Therefore, the breadth of the rectangular plot is 20 m.
Perimeter of a rectangle = 2 x (l + b)
               = 2 x (22 + 20)
               = 2 x 42
               = 84 m
Therefore, the perimeter of the rectangular plot is 84 m.

Question 4: The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.
Answer:
Given
Perimeter of rectangular sheet = 100 cm
Length of rectangular sheet = 35 cm
To find = Breadth
        Area
Perimeter of rectangle = 2 x (l + b)
              100 = 2 x (35 + b)
              100 = (2 x 35) + (2 x b)
                      100 = 70 + 2b
                        2b = 100 - 70 = 30
                        2b = 30
                          b = 30/2
                          b = 15 m
Therefore, the breadth of the rectangular sheet is 15 m.
Area of rectangle = l x b
             = 35 x 15
             = 525 m²
Therefore, the area of rectangular sheet is 525 m².

Question 5: The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.
Answer:

Given
Area of Square park = Area of rectangular park
Length of side of square park = 60 m
Length of rectangular park = 90 m
To find = Area
        Breadth
Area of square = side x side
        = 60 x 60
        = 3600 m²
Breadth of rectangle = area/length
                                 = 3600/90  
                                 = 40 m
Therefore, the breadth of rectangular park is 40 m.

Question 6: A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also find which shape encloses more area?
Answer:
Given
Length of rectangle = 40 cm
Breadth of rectangle = 22 cm
To find = Perimeter
        Side of square
        Which shape encloses more area
Perimeter of rectangle = 2 x (l + b)
             = 2 x (40 + 22)
            = 2 x 62
            = 124 cm
Therefore, the perimeter of rectangle is 124 cm.
Perimeter of Square = Perimeter of Rectangle
Length of side of square = perimeter/4
                = 124/4
                = 31 cm
Therefore, the length of side of square is 31 cm.
Area of rectangle = length x breadth
             = 40 x 22
             = 880 cm²
Area of square = side x side
         = 31 x 31
         = 961 cm²
Compare
880 cm² < 961 m²
Therefore, square encloses more area.

Question 7: The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.
Answer:
Given
Perimeter of rectangle = 130 m
Breadth = 30 cm
To find = Length
     = Area
Perimeter of rectangle = 2 x (l + b)
              130 = 2 x (l + 30)
              130 = (2 x l) + (2 x 30)
                      2l = 130 - 60
                      2l = 70
              l = 70/2
              l = 35
Therefore, length of a rectangle is 35 cm.
Area of rectangle = l x b
             = 35 x 30
             = 1050 cm²
Therefore, the area of rectangle is 1050 cm².

Question 8: A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m. Find the cost of white washing the wall, if the rate of white washing the wall is ₹ 20 per m
².
Answer:

Given
Length of wall = 4.5 m
Breadth of wall = 3.6 m
Door length = 2 m
Door breadth = 1 m
Rate of white washing = ₹ 20 per m²
To find = Area to be white washed
     = Cost of white washing
Area of rectangle = l x b
             = 4.5 x 3.6
             = 16.2 m²
Therefore, the area of wall = 16.2 m².
Area of rectangle = l x b
             = 2 x 1
             = 2 m²
Therefore, the area of door is 2 m².
Area to be white washed = area of wall - area of door
                = 16.2 m² - 2 m²
                = 14.2 m²
Therefore, the area to be white washed is 14.2 m².
Cost of white washing 1 m² = ₹ 20
Cost of white washing 14.2 m² = ?
= 20 x 14.2
= ₹ 284
Therefore, the cost of white washing the wall is ₹ 284.

No comments:

Post a Comment

Also read!

Class 6 Solutions

• Class 7

Class 7 Computer Kips Solutions
Class 7 Gul Mohar English Solutions
English Grammar Class 7
English Writing Skills Class 7
Class 7 Map Pointing Solutions
Class 7 NCERT Civics Solutions
Class 7 NCERT Civics Notes
Class 7 NCERT Civics Extra Questions
Class 7 NCERT Geography Solutions
Class 7 NCERT Geography Notes
Class 7 NCERT Geography Extra Questions
Class 7 NCERT History Solutions
Class 7 NCERT History Notes
Class 7 NCERT History Extra Questions
Class 7 NCERT Maths Solutions
Class 7 NCERT Science Solutions
Class 7 NCERT Science Notes
Class 7 NCERT Science Extra Questions

• Class 8

Class 8 Kips Artificial Intelligence Solutions
Class 8 Gul Mohar English Solutions
English Grammar Class 8
English Writing Skills Class 8
Class 8 Map Pointing Solutions
Class 8 NCERT Civics Solutions
Class 8 NCERT Civics Notes
Class 8 NCERT Civics Extra Questions
Class 8 NCERT Geography Solutions
Class 8 NCERT Geography Notes
Class 8 NCERT Geography Extra Questions
Class 8 NCERT History Solutions
Class 8 NCERT History Notes
Class 8 NCERT History Extra Questions
Class 8 NCERT Maths Solutions
Class 8 NCERT Science Solutions
Class 8 NCERT Science Notes
Class 8 NCERT Science Extra Questions
Class 8 NCERT Science Exemplar
Class 8 NCERT Science MCQs

Class 9 Solutions

• Class 10

Class 10 Kips Artificial Intelligence Solutions
Class 10 NCERT English Solutions
→ Class 10 Map Pointing Solutions
Class 10 NCERT Civics Solutions
Class 10 NCERT Civics Notes
Class 10 NCERT Civics Extra Questions
Class 10 NCERT Geography Solutions
Class 10 NCERT Geography Notes
Class 10 NCERT Geography Extra Questions
Class 10 NCERT History Solutions
→ Class 10 NCERT History Notes
Class 10 NCERT History Extra Questions
Class 10 NCERT Maths Solutions
Class 10 NCERT Science Solutions
Class 10 NCERT Science Notes
Class 10 NCERT Science Extra Questions

• Computer languages
Python Basics

• Extra Activities
Extra Activities

• Extra Knowledge
Extra Information
General Knowledge
Historical Places in India
Latest technology
Physical Sciences
Facts

• Mathematics quick links
Mathematical Terms
Maths Tricks

CONTACT US