NCERT Solutions for Class 7 Maths Chapter 11 Exercise 11.1 (Ex. 11.1) Perimeter and Area updated for academic session 2022-2023 in Hindi and English Medium. All the questions are solved by subject experts using step by step derivation. In class 7 math exercise 11.1 we will learn to solve the questions based on perimeter and areas of square and rectangles. Questions given in exercises are easy to solve, just need to understand the concepts.
Class 7 Maths Chapter 11 Exercise 11.1 Solution
CBSE NCERT Class 7 Maths Chapter 11 Exercise 11.1 Solution in Hindi and English Medium
|Chapter: 11||Perimeter and Area|
|Exercise: 11.1||Hindi and English Medium Solution|
Class 7 Maths Chapter 11 Exercise 11.1 Solution in Videos
Area and Perimeter of a Rectangle
Consider a rectangle with length = l units and breadth = b units. Then, we have:
(i) Area of the rectangle = (l x b) sq units
(ii) Length = units.
(iii)Breadth = units. (iv)Diagonal = units.
Area of 4 Walls of a Room
Let there be a room with length = l units, breadth = b units, height = h units. Then, we have:
(i) Area of the 4 walls = [2 (l + b) x h] sq units.
(ii) Diagonal of the room = √(l2 + b2 + h2) units.
Area and Perimeter of a Square
Let there be a square each of whose sides measures a units.
Then, we have:
(i) Area of the square = a2 sq units.
(ii) Side of the square = (√(area) units.
(iii) Diagonal of the square = (√2a) units.
(iv) Area of the square = ½ x (diagonal)2 sq units.
(v) Perimeter of the square = (4a) units.
Class 7 Maths Exercise 11.1 Extra Questions
The length and breadth of a rectangular field are 120 m and 75 m respectively. Find (i) the area of the field and the cost of turfing it at Rs. 15 per m². (ii) the perimeter of the field and the cost of fencing it at Rs. 40 per m.
Length of the field = 120 m and its breadth = 75 m.
(i) Area of the field = (120 x 75) m = 9000 m².
Cost of turfing of the field = Rs. (9000 x 15)
= Rs. 135000.
(ii) Perimeter of the field = 2 x (l + b) units = 2 x (120 + 75) m = (2 x 195) m = 390 m.
The length and breadth of a rectangular field are in the ratio 3 : 2. If the area of the field is 3456 m², find the cost of fencing it at Rs. 60 per m.
According length and breadth ratio, let the length of the field be 3x m. Then, its breadth = 2x m.
So, area of the field = (3x X 2x) m² = (6×2) m².
But, area = 3456 m² (given)
So, 6x² = 3456 m²
Or, x² = 576 m²
Or, x = = 24 m. length = (3 x 24) m = 72 m and breadth = (2 x 24) m = 48 m.
So, perimeter of the field
= 2 x (l + b) units = 2 x (72 + 48) m = (2 x 120) m = 240 m.
So, the cost of fencing = Rs. (240 x 60) = Rs. 1400.
Class 7 Maths Exercise 11.1 Important Questions
Where do we use perimeter and area in real life?
Uses of perimeter and area in daily life
(i) Fencing off an area to plot a crop. Since fences cost money for a given area you would (ii) want to minimize the perimeter.
(iii) Planning the construction of a house.
(iv) Building a barn with box stalls for horses.
(v) Making Wooden furniture.
(vi) Building a swimming pool.
How does perimeter relate to area?
The perimeter is the sum of all the side lengths of a shape. The area is the amount of two dimensional space a shape occupies.
What do area and perimeter have in common?
In geometry, area is the 2-dimensional space or region occupied by a closed figure, while perimeter is the distance around a closed figure i.e. the length of the boundary. For example, the area can be used to calculate the size of the carpet to cover the whole floor of a room.