Solution of NCERT Exercise 11.1

Perimeter and Area 7th Math

Solution of NCERT 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 1m2 of the land costs Rs 10,000.

Solution:

(i) Its area

Given,

Length of the rectangular park = 500 m

Breadth of the rectangular park = 300 m

∴ Area of rectangular park = ?

We know that,

Area of a rectangle = Length × Breadth

∴ Area of given rectangular park = 500 m × 300 m

∴ Area of rectangular park = 150000 m2 Answer.

(ii) The cost of the land, if 1 m2 of the land costs Rs. 10,000.

∵ Cost of 1 m2 of land = Rs 10, 000.

∴ Cost of 150000 m2 of land = Rs 10,000 × 150000

= Rs 1500000000.00

∴ Cost of land = Rs 1500000000.00 Answer.

Question (2) Find the area of a square park whose perimeter is 320 m.

Solution:

Given,

Perimetre of square park = 320 m

∴ Area of that square park = ?

Let side of given square park = a

We know that;

Perimetre of a square = 4 × side.

⇒ 320 m = 4 × a

⇒ 4 × a = 320 m

⇒ a = `320/4` m = 80 m

Thus side of give square park = 80 m

Now we know that,

Area of a square = side2

∴ Area of given square park = (80 m)2

= 80 m × 80 m

= 6400 m2

∴ Area of given square park = 6400 m2 Answer.

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.

Solution:

Given,

Area of the rectangular park = 440 m2

And, Length of that rectangular park = 22 m

∴ Breadth of the rectangular park = ?

Let Breadth of given rectangular park = b

We know that,

Area of a rectangle = Length × Breadth

⇒ 440 m2 = 22m × b

⇒ 22 m × b = 440 m2

`=> b = (440 m^2)/(22 m)`

⇒ b = 20 m

We know, that

Perimeter of rectangle = 2(Length + Breadth)

Thus, perimeter of given rectangular plot = 2(22 m + 20 m)

=2 × 42 m

= 84 m

Thus, perimeter of given rectangular plot = 84 m

∴ Breadth of the given rectangular park = 20 m and Perimeter = 84 m  Answer.

Question (4) The perimetre of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

Solution:

Given,

Perimetre of the rectangular sheet = 100 cm

And, Length of that sheet = 35 cm

∴ Breadth and area of that sheet = ?

Let breadth of the given rectangular sheet = b

We know that,

Perimetre of a rectangle = 2 ( Length + Breadth)

⇒ 100 cm = 2(35 cm + b)

⇒ 100 cm = 70 cm + 2p

⇒ 70 cm + 2b = 100 cm

⇒ 2b = 100 cm – 70 cm

⇒ 2b = 30 cm

⇒ b = `30/2` cm = 15 cm

∴ Breadth of given sheet = 15 cm

Now, we know that,

Area of rectangle = Length × Breadth

∴ Area of given rectangular sheet = 35 cm × 15 cm

= 525 cm2

Therefore, Breadth of given sheet = 15 cm; and area of that rectangular sheet = 525 cm2 Answer.

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.

Solution:

Given,

Side of the square park = 60 m

Length of the rectangular park = 90 m

Area of the square park = Area of the rectangular park.

∴ Breadth of rectangular park = ?

We know that,

Area of a square = Side2

∴ Area of given square park = (60 m)2

= 60 m × 60 m

= 3600 m2

Let Breadth of the given rectangle park = b

Now, we know that,

Area of a rectangle = Length × Breadth

∴ Area of given rectangular park = 90 m × b

⇒ 3600 m2 = 90 m × b

[∵ As per question, area of rectangular park = area of square park = 3600 m2 (As calculated above)]

⇒ 90 m × b = 3600 m2

`:. b = (3600 m^2)/(90 m)=40m`

∴ Breadth of given rectangular park = 40 m Answer.

Question (6) A wire is in the shape of 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 its side? Also find which shape encloses more area?

Solution:

Given,

Length of the rectangle = 40 cm.

And, Breadth = 22 cm.

Then the side of the square made after rebent of same wire from which rectangle was made = ?

We know that,

Perimetre of rectangle = 2 (Length + Breadth)

= 2(40 cm + 22 cm)

= 2 × 62 cm

= 124 cm

∴ Perimetre of the rectangle = 124 cm.

Since, square is made after rebending of same wire

∴ Perimetre of square = Perimetre of the rectangle.

Now, we know that,

Perimetre of a square = 4 × side.

⇒ 124 cm = 4 × side

[ ∵ Perimetre of the square = Perimetre of the rectangle = 124 cm]

⇒ 4 × side = 124 cm

⇒ side = `124/4` cm = 31 cm

Thus, side of square = 31 cm.

Now, Area of square = side2

∴ Area of given square = (31 cm )2

= 31 cm × 31 cm

= 961 cm2

And, we know that,

Area of Rectangle = Length × Breadth

Thus, area of given rectangle = 40 cm &# 215; 22 cm

= 880 cm 2

Therefore,

Side of square = 31 cm. And square will enclose more area. Answer

Question (7) The perimetre 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.

Solution:

Given,

Perimetre of Rectangle = 130 cm

Breadth of rectangle = 30 cm

Length = ?

And area = ?

Let Length of the rectangle = m

We know that ,

Perimetre of a rectangle = 2 (Length + Breadth)

⇒ 130 cm = 2(m + 30 cm)

⇒ 130 cm = 2m + 60 cm.

⇒ 2m + 60 cm = 130 cm

⇒ 2 m = 130 – 60 cm

⇒ 2 m = 70 cm

⇒ m = `70/2 `=35 cm.

∴ Legth of therectangle= 35 cm.

Now we know that area of rectangle = Length × Breadth

Thus area of given rectangle = 35 cm × 30 cm

= 1050 cm2

Thus, length f the rectangle = 35 cm; and area of the rectangle =1050 cm2 Answer

Question (8) A door of length 2m and breadth 1m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m (figure). Find the cost of white washing the wall, if the rate of white washing the wall is Rs 20 per m2.

class 7th math Perimeter and area exercise 11.1 question8

Solution:

Given,

Length of wall = 4.5 m

Breadth of wall = 3.6 m

Length of door = 2m

Breadth of door = 1 m

Rate of white washing = Rs 20 per m2

∴ Total cost of white washing of wall =?

We know that,

Area of a rectangle = Length × Breadth

∴ Area of wall = 4.5 m × 3.6 m

= 16.20 m2

Now, Area of the door = length × breadth

= 2m × 1m

=2 m2

Now surface area of wall excluding the door

= Area of wall including the door – Area of door

= 16.2 m2 – 2 m2

= 14.2 m2

Thus Area of wall excluding door = 14.2 m2

Now,

∵ Cost of white washing of 1 m2 = Rs 20.00

∴ Cost of white washing of 14.2 m2

= Rs 20.00 × 14.2

= Rs 284.00

∴ Cost of white washing of wall = Rs 284.00 Answer

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