Students can Download Chapter 11 Perimeter and Area Ex 11.1, Question and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths, Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.

## Karnataka State Syllabus Class 7 Maths Chapter 11 Perimeter and Area Ex 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

Solution:

Length of the land = l = 500 m

Breadth of the land = b = 300 m

∴ The Area of rectangular piece of land

l × b = 500 × 300

= 150,000 Sq. m.

ii) The cost of the. land, if 1 m^{2} of the land costs 10,000.

Solution:

The cost of rectangular piece of land per

1 Sq m = ₹ 10,000

∴ Total cost of that land = 150,000 × 10,000 = ₹ 1,500,000,000

Question 2.

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

Solution:

Perimeter of the sq park = 320 m

∴ One side of the sq part = \(\frac{320}{4}\) = 80 m

∴ Area of the square park = a^{2} = side^{2} = 80^{2}

80 × 80 = 6400 Sq.m

Question 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:

Area of a rectangular filed = l × b = 440 sq m.

Length of a rectangular field =

perimeter of the rectangular filed = 2(l + b)

2 (20 + 22)

2(42) = 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.

Solution:

Perimeter of the rectangular sheet = 100 cm

length of the rectangular sheet = 35 cm

Breadth of the rectangular sheet = 2(l + b) = 100

= 2(35 + b)= 100

= 70 + 2b = 100

= 2b = 100 – 70

Breadth = 15 cms

∴ Area = l × b = 35 × 15 = 525 sq.cms

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:

Area of the sq park = Area of rectangular park

a = side = 60 m

a^{2} = l × b

60^{2} = 90 × b

3600 = 90 × b

∴ The breadth of a rectangular park = 40 mts.

Question 6.

A wire is 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:

The shape of the wire rectangle.

The perimeter of this rectangle

Total or length of wire =2 (l + b)

length = 40 cm breadth = 22 cm

= 2(40 + 22)

= 2(62) = 124 cm.

If it is reshaped in the form of sq, its side}

∴ Its square = side × side = 31 × 31 = 961 sq. cms

Rectangle’s Area = l × b = 40 × 22 = 880 sq.cms.

The area of the square encloses more area than the area of the rectangle.

Question 7.

The perimeter of a rectangle is 130 cm. If the breadth of the rectangle 30 cm, find its length. Also find the area of the rectangle.

Solution:

p = perimeter of a rectangle = 130 cm

l = length of a rectangle = l = ?

b = breadth of a rectangle = b = 30 cm

p = 2 (l + b)

130 = 2l + 2 × 30

2l = 130 – 60 = 70

∴ Area of a rectangle = l × b = 30 × 35

= 1050 sq.cms

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 (Fig 11.6). Find the cost of whitewashing the wall, if the rate of whitewashing the wall is ₹ 20 per m^{2}

Solution:

Area of the wall = l × b

length of the wall = 4.5 m

the breadth of the wall = 3.6 m

Area = 4.5 × 3.6 = 16.2 sq.m

length of the door = 2 m

the breadth of the door = 1 m

Area of the door = 2 × 1 = 2 sq. m

Area of the wall excluding (without) door = 16.20 – 2 = 14.20 sq.m

Rate of whitewashing the wall = Rs. 20/ sq.m

∴ The total cost of whitewashing the wall = 14.20 × 20 = Rs. 284.00