Exercise 10.2
1. Find the areas of the following figures by counting squares.
(i)
(i) 50 cm and 20 cm
Solution:
Area of a Rectangle :
Length of the rectangle =
Breadth of the rectangle =
Area of the rectangle =
=
Therefore Area =
(ii)
(ii) 65 in and 45 in
Solution:
Area of a Rectangle
Length of the rectangle =
Breadth of the rectangle =
Area of the rectangle =
=
Therefore Area =
(iii)
(iii) 25 cm and 16 cm
Solution:
Area of a Rectangle
Length of the rectangle =
Breadth of the rectangle =
Area of the rectangle =
=
Therefore area =
(iv)
(iv) 7 km and 19 km
Solution:
Area of a Rectangle
Length of the rectangle =
Breadth of the rectangle =
Area of the rectangle =
=
Therefore area =
2. Find the areas of the following squares.
(i)
(i) 26 m
Solution:
Area of a Square:
Side of the square =
Area of the square =
=
Therefore, Area =
(ii)
(ii) 17 km
Solution:
Area of a Square:
Side of the square =
Area of the square =
=
Therefore, Area =
(iii)
(iii) 52 cm
Solution:
Area of a Square:
Side of the square =
Area of the square =
=
Therefore, Area =
(iv)
(iv) 8 cm
Solution:
Area of a Square:
Side of the square =
Area of the square =
=
Therefore, Area =
3. The area of rectangular frame is 1,125 sq. cm. If its width is 25 cm, what is its length ?
Solution:
Area of rectangular frame =
Width of the frame =
Area of rectangular frame = length × width
Length =
=
4. The length of a rectangular field is 60 m and the breadth is half of its length. Find the area of the field.
Solution:
Length of the rectangular field =
Breadth of the field =
Area of the rectangular field =
=
5. A square sheet of paper has a perimeter of 40 cm. What is the length of its side? Also, find the area of the square sheet.
Solution:
Perimeter of the square =
Perimeter formula:
Side =
Area of the square =
=
6. The area of a rectangular plot is 2400 sq. meters, and its length is 1.5 times its breadth. What is the perimeter?
Solution:
Area of rectangular plot =
Let the breadth be x m, then length =
Area formula:
Solving for x:
Perimeter of rectangle =
= 2 × (
7. A rectangular room is 6 m long and 4 m wide. How many square meters of carpet is required to cover the floor? If carpet costs ₹240 per sq. meter, what is the total cost?
Solution:
Length of the room =
Area of the floor =
=
Cost per sq. m of carpet = ₹
Total cost = 24 × 240 = ₹
8. Two fields have the same perimeter. One is a square of side 72 m, and another is a rectangle of length 80 m. Which field has a greater area and by how much?
Solution:
Side of square field =
Area of square field =
= 72 × 72 =
Length of rectangular field =
Perimeter formula: 2(l + b) =
Solving for breadth: b =
Area of rectangular field =
=
Difference in area =
The area of square field is greater than that of rectangular field by 64 sq. m
9. The area of a square is 49 sq. cm. A rectangle has the same perimeter as the square. If the length of the rectangle is 9.3 cm, what is its breadth? Also, which has the greater area?
Solution:
Area of the square =
Side of the square =
Perimeter of the square = 4 ×
= 4 ×
Perimeter of the rectangle =
Perimeter formula: 2(l + b) =
Given length of rectangle =
Solving for breadth: b = 14 - 9.3 =
Area of the rectangle =
=
Since
10. Rahul owns a rectangular field of length 400 m and breadth 200 m. His friend Ramu owns a square field of length 300 m. Find the cost of fencing the two fields at ₹ 150 per meter. If one tree can be planted in an area of 10 sq. m, who can plant more trees in his field? How many more trees can he plant?
Solution:
Length of the rectangular field of Rahul =
Breadth of the rectangular field of Rahul =
Perimeter of rectangular field of Rahul = 2 × (length + breadth)
= 2 × (400 + 200) = 2 ×
Side of the square field of Ramu =
Perimeter of square field of Ramu =
= 4 ×
Total length of the wire to be fenced = 1200 + 1200 =
Cost of fencing 1 meter = Rs.
Cost of fencing 2400 meters = 2400 × 150 = Rs.
Cost of fencing Ramu’s field = 1200 × 150 = Rs.
Area of Rahul’s field =
= 400 × 200 =
A tree occupies an area of
Number of trees that can be planted in Rahul’s field =
Area of Ramu’s field =
= 300 × 300 =
Number of trees that can be planted in Ramu’s field =
Ramu can plant
11. The length of a rectangular floor is 20 m more than its breadth. If the perimeter of the floor is 280 m, what is its length?
Solution:
Let the breadth of the rectangular field =
Therefore the length of the rectangular field = x +
Perimeter of the rectangular field = 2(length + breadth) = 2(
= 2(
By problem, 4x + 40 =
Solving for x: 4x = 280 -
x =
The breadth of the rectangular field =
The length of the rectangular field =
Therefore the length of the Rectangular field is 80 m
12. A rectangular plot of land is 240 m by 200 m. The cost of fencing per meter is ₹ 30. What is the cost of fencing the entire field?
Solution:
The dimensions of the rectangular plot of land are
Perimeter of the plot of land =
= 2 ×
Cost of fencing 1 meter = ₹
Cost of fencing 880 meters =
Therefore the Cost of fencing 880 meters = ₹ 26400
13. The side of a square field is 120 meters. The cost of preparing a grass lawn is ₹ 35 per square meter. How much will it cost if the entire field is converted into a lawn?
Solution:
The side of the square field =
Area of the square field =
=
Cost of preparing 1 sq m or
Cost of converting the entire field (14400
Total cost =
Therfore the cost of the entire field converted into a lawn is 504000
14. What will happen to the area of a rectangle, if:
(i)
(i) Its length and breadth are doubled?
Solution:
Let the length of a rectangle be
Original area =
When both length and breadth are doubled
New length =
New area =
∴ The area increases by
(ii)
(ii) Its length is doubled and breadth is tripled?
When length is
New length =
New area =
Therefore The area increases by
15. What will happen to the area of a square if its side is:
(i)
(i) Doubled?
Solution:
Let the side of a square be
Area of the square =
If the side is doubled, it becomes x + x =
Area of the square =
Therefore the area increases by
(ii)
(ii) Halved?
Solution:
If the side of the square is halved, it becomes
Area of the square =
Therefore the area of the square becomes