NCERT Solutions for Class 7 Maths Exercise 11.1 Chapter 11 Perimeter and Area in simple PDF are available here. In this exercise NCERT Solutions for Class 7 Chapter 11 students are going to recall how to calculate the length, breadth, perimeter and areas of square and rectangle. Learn more about these topics by solving the questions of NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area with the help of solutions provided here.

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**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 m ^{2} of the land costs â‚¹ 10,000.**

**Solution:-**

From the question it is given that,

Length of the rectangular piece of land = 500 m

Breadth of the rectangular piece of land = 300 m

Then,

(i) Area of rectangle = Length Ã— Breadth

= 500 Ã— 300

= 150000 m^{2}

(ii) Cost of the land for 1 m^{2} = â‚¹ 10000

Cost of the land for 150000 m^{2} = 10000 Ã— 150000

= â‚¹ 1500000000

**2. Find the area of a square park whose perimeter is 320m.**

**Solution:-**

From the question it is given that,

Perimeter of the square park = 320 m

4 Ã— Length of the side of park = 320 m

Then,

Length of the side of park = 320/4

= 80 m

So, Area of the square park = (length of the side of park)^{2}

= 80^{2}

= 6400 m^{2}

**3. Find the breadth of a rectangular plot of land, if its area is 440 m ^{2} and the length is 22 m. Also find its perimeter.**

**Solution:-**

From the question it is given that,

Area of the rectangular plot = 440 m^{2}

Length of the rectangular plot = 22 m

We know that,

Area of the rectangle = Length Ã— Breadth

440 = 22 Ã— Breadth

Breadth = 440/22

Breadth = 20 m

Then,

Perimeter of the rectangle = 2(Length + Breadth)

= 2 (22 + 20)

= 2(42)

= 84 m

âˆ´Perimeter of the rectangular plot is 84 m.

**4. The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.**

**Also find the area.**

**Solution:-**

From the question it is given that,

Perimeter of the a rectangular sheet = 100 cm

Length of the rectangular sheet = 35 cm

We know that,

Perimeter of the rectangle = 2 (Length + Breadth)

100 = 2 (35 + Breadth)

(100/2) = 35 + Breadth

50 â€“ 35 = Breadth

Breadth = 15 cm

Then,

Area of the rectangle = Length Ã— Breadth

= 35 Ã— 15

= 525 cm^{2}

âˆ´Area of the rectangular sheet is 525 cm^{2}

**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:-**

From the question it is given that,

Area of a square park is the same as of a rectangular park.

Side of the square park = 60 m

Length of the rectangular park = 90 m

We know that,

Area of the square park = (one of the side of square)^{2}

= 60^{2}

= 3600 m^{2}

Area of the rectangular park = 3600 m^{2} â€¦ [âˆµ given]

Length Ã— Breadth = 3600

90 Ã— Breadth = 3600

Breadth = 3600/90

Breadth = 40 m

**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?**

**Solution:-**

By reading the question we can conclude that, perimeter of the square is same as perimeter of rectangle.

From the question it is given that,

Length of the rectangle = 40 cm

Breadth of the square = 22 cm

Then,

Perimeter of the rectangle = Perimeter of the Square

2 (Length + Breadth) = 4 Ã— side

2 (40 + 22) = 4 Ã— side

2 (62) = 4 Ã— side

124 = 4 Ã— side

Side = 124/4

Side = 31 cm

So, Area of the rectangle = (Length Ã— Breadth)

= 40 Ã— 22

= 880 cm^{2}

Area of square = side^{2}

= 31^{2}

= 31 Ã— 31

= 961 cm^{2}

âˆ´Square shaped wire encloses more area.

**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.**

**Solution:-**

From the question it is given that.

Perimeter of the rectangle = 130 cm

Breadth of the rectangle = 30

We know that,

Perimeter of rectangle = 2 (Length + Breadth)

130 = 2 (length + 30)

130/2 = length + 30

Length + 30 = 65

Length = 65 â€“ 30

Length = 35 cm

Then,

Area of the rectangle = Length Ã— Breadth

= 35 Ã— 30

= 1050 cm^{2}

**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 (Fig). Find the cost of white washing the wall, if the rate of white washing the wall is â‚¹ 20 per m ^{2}. **

** **

**Solution:-**

From the question it is given that,

Length of the door = 2 m

Breadth of the door = 1 m

Length of the wall = 4.5 m

Breadth of the wall = 3.6 m

Then,

Area of the door = Length Ã— Breadth

= 2 Ã— 1

= 2 m^{2}

Area of the wall = Length Ã— Breadth

= 4.5 Ã— 3.6

= 16.2 m^{2}

So, Area to be white washed = 16.2 â€“ 2 = 14.2 m^{2}

Cost of white washing 1 m^{2} area = â‚¹ 20

Hence cost of whit washing 14.2 m^{2}Â area = 14.2 Ã— 20

= â‚¹ 284