Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Mensuration – I (Perimeter and Area of Rectilinear Figures Exercise 20.1)
Mensuration – I (Perimeter and Area of Rectilinear Figures Exercise 20.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download
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Page 1
1. Find the area, in square metres, of a rectangle whose
(i) Length = 5.5 m, breadth = 2.4 m
(ii) Length = 180 cm, breadth = 150 cm
Solution:
(i) Given Length = 5.5 m, Breadth = 2.4 m
We know that area of rectangle = Length x Breadth
= 5.5 m x 2.4 m = 13.2 m
2
(ii) Given Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [Since 100 cm = 1 m]
We know that area of rectangle = Length x Breadth
= 1.8 m x 1.5 m = 2.7 m
2
2. Find the area, in square centimetres, of a square whose side is
(i) 2.6 cm
(ii) 1.2 dm
Solution:
(i) Given side of the square = 2.6 cm
We know that area of the square = (Side)
2
= (2.6 cm)
2
= 6.76 cm
2
(ii) Given side of the square = 1.2 dm
= 1.2 x 10 cm = 12 cm [Since 1 dm = 10 cm]
We know that area of the square = (Side)
2
= (12 cm)
2
= 144 cm
2
3. Find in square meters, the area of a square of side 16.5 dam.
Solution:
Given side of the square = 16.5
dam = 16.5 x 10 m = 165 m [Since 1 dam/dm (decametre) = 10 m]
Page 2
1. Find the area, in square metres, of a rectangle whose
(i) Length = 5.5 m, breadth = 2.4 m
(ii) Length = 180 cm, breadth = 150 cm
Solution:
(i) Given Length = 5.5 m, Breadth = 2.4 m
We know that area of rectangle = Length x Breadth
= 5.5 m x 2.4 m = 13.2 m
2
(ii) Given Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [Since 100 cm = 1 m]
We know that area of rectangle = Length x Breadth
= 1.8 m x 1.5 m = 2.7 m
2
2. Find the area, in square centimetres, of a square whose side is
(i) 2.6 cm
(ii) 1.2 dm
Solution:
(i) Given side of the square = 2.6 cm
We know that area of the square = (Side)
2
= (2.6 cm)
2
= 6.76 cm
2
(ii) Given side of the square = 1.2 dm
= 1.2 x 10 cm = 12 cm [Since 1 dm = 10 cm]
We know that area of the square = (Side)
2
= (12 cm)
2
= 144 cm
2
3. Find in square meters, the area of a square of side 16.5 dam.
Solution:
Given side of the square = 16.5
dam = 16.5 x 10 m = 165 m [Since 1 dam/dm (decametre) = 10 m]
Area of the square = (Side)
2
= (165 m)
2
= 27225 m
2
4. Find the area of a rectangular field in acres whose sides are:
(1) 200 m and 125 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 200 m
Breadth of the rectangular field = 125 m
We know that area of the rectangular field = Length x Breadth
= 200 m x 125 m
= 25000 m
2
= 250 acres [Since 100 m
2
= 1 acre]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 90.6 acres [Since 100 m
2
= 1 acre]
5. Find the area of a rectangular field in hectares whose sides are:
(i) 125 m and 400 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 125 m
Breadth of the rectangular field = 400 m
We know that the area of the rectangular field = Length x Breadth
= 125 m x 400 m
= 50000 m
2
= 5 hectares [Since 10000 m
2
= 1 hectare]
Page 3
1. Find the area, in square metres, of a rectangle whose
(i) Length = 5.5 m, breadth = 2.4 m
(ii) Length = 180 cm, breadth = 150 cm
Solution:
(i) Given Length = 5.5 m, Breadth = 2.4 m
We know that area of rectangle = Length x Breadth
= 5.5 m x 2.4 m = 13.2 m
2
(ii) Given Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [Since 100 cm = 1 m]
We know that area of rectangle = Length x Breadth
= 1.8 m x 1.5 m = 2.7 m
2
2. Find the area, in square centimetres, of a square whose side is
(i) 2.6 cm
(ii) 1.2 dm
Solution:
(i) Given side of the square = 2.6 cm
We know that area of the square = (Side)
2
= (2.6 cm)
2
= 6.76 cm
2
(ii) Given side of the square = 1.2 dm
= 1.2 x 10 cm = 12 cm [Since 1 dm = 10 cm]
We know that area of the square = (Side)
2
= (12 cm)
2
= 144 cm
2
3. Find in square meters, the area of a square of side 16.5 dam.
Solution:
Given side of the square = 16.5
dam = 16.5 x 10 m = 165 m [Since 1 dam/dm (decametre) = 10 m]
Area of the square = (Side)
2
= (165 m)
2
= 27225 m
2
4. Find the area of a rectangular field in acres whose sides are:
(1) 200 m and 125 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 200 m
Breadth of the rectangular field = 125 m
We know that area of the rectangular field = Length x Breadth
= 200 m x 125 m
= 25000 m
2
= 250 acres [Since 100 m
2
= 1 acre]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 90.6 acres [Since 100 m
2
= 1 acre]
5. Find the area of a rectangular field in hectares whose sides are:
(i) 125 m and 400 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 125 m
Breadth of the rectangular field = 400 m
We know that the area of the rectangular field = Length x Breadth
= 125 m x 400 m
= 50000 m
2
= 5 hectares [Since 10000 m
2
= 1 hectare]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that the area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 0.906 hectares [Since 10000 m
2
= 1 hectare]
6. A door of dimensions 3 m x 2m is on the wall of dimension 10 m x 10 m. Find the
cost of painting the wall if rate of painting is Rs 2.50 per sq. m.
Solution:
Given length of the door = 3 m
Also given that breadth of the door = 2 m
Side of the wall = 10 m
We know that Area of the square = (Side)
2
Area of the wall = Side x Side = 10 m x 10 m
= 100 m
2
We know that the area of the rectangle = length x breadth
Area of the door = Length x Breadth = 3 m x 2 m = 6 m
Thus, required area of the wall for painting = Area of the wall – Area of the door
= (100 – 6) m
2
= 94 m
2
Rate of painting per square metre = Rs. 2.50
Hence, the cost of painting the wall = Rs. (94 x 2.50) = Rs. 235
7. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the
same wire is bent in the shape of a square, what will be the measure of each side.
Also, find which side encloses more area?
Solution:
Given length of rectangular shaped wire = 40cm
Breadth of rectangular shaped wire = 22cm
Perimeter of the rectangle = 2(Length + Breadth)
= 2(40 cm + 22 cm)
Page 4
1. Find the area, in square metres, of a rectangle whose
(i) Length = 5.5 m, breadth = 2.4 m
(ii) Length = 180 cm, breadth = 150 cm
Solution:
(i) Given Length = 5.5 m, Breadth = 2.4 m
We know that area of rectangle = Length x Breadth
= 5.5 m x 2.4 m = 13.2 m
2
(ii) Given Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [Since 100 cm = 1 m]
We know that area of rectangle = Length x Breadth
= 1.8 m x 1.5 m = 2.7 m
2
2. Find the area, in square centimetres, of a square whose side is
(i) 2.6 cm
(ii) 1.2 dm
Solution:
(i) Given side of the square = 2.6 cm
We know that area of the square = (Side)
2
= (2.6 cm)
2
= 6.76 cm
2
(ii) Given side of the square = 1.2 dm
= 1.2 x 10 cm = 12 cm [Since 1 dm = 10 cm]
We know that area of the square = (Side)
2
= (12 cm)
2
= 144 cm
2
3. Find in square meters, the area of a square of side 16.5 dam.
Solution:
Given side of the square = 16.5
dam = 16.5 x 10 m = 165 m [Since 1 dam/dm (decametre) = 10 m]
Area of the square = (Side)
2
= (165 m)
2
= 27225 m
2
4. Find the area of a rectangular field in acres whose sides are:
(1) 200 m and 125 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 200 m
Breadth of the rectangular field = 125 m
We know that area of the rectangular field = Length x Breadth
= 200 m x 125 m
= 25000 m
2
= 250 acres [Since 100 m
2
= 1 acre]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 90.6 acres [Since 100 m
2
= 1 acre]
5. Find the area of a rectangular field in hectares whose sides are:
(i) 125 m and 400 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 125 m
Breadth of the rectangular field = 400 m
We know that the area of the rectangular field = Length x Breadth
= 125 m x 400 m
= 50000 m
2
= 5 hectares [Since 10000 m
2
= 1 hectare]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that the area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 0.906 hectares [Since 10000 m
2
= 1 hectare]
6. A door of dimensions 3 m x 2m is on the wall of dimension 10 m x 10 m. Find the
cost of painting the wall if rate of painting is Rs 2.50 per sq. m.
Solution:
Given length of the door = 3 m
Also given that breadth of the door = 2 m
Side of the wall = 10 m
We know that Area of the square = (Side)
2
Area of the wall = Side x Side = 10 m x 10 m
= 100 m
2
We know that the area of the rectangle = length x breadth
Area of the door = Length x Breadth = 3 m x 2 m = 6 m
Thus, required area of the wall for painting = Area of the wall – Area of the door
= (100 – 6) m
2
= 94 m
2
Rate of painting per square metre = Rs. 2.50
Hence, the cost of painting the wall = Rs. (94 x 2.50) = Rs. 235
7. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the
same wire is bent in the shape of a square, what will be the measure of each side.
Also, find which side encloses more area?
Solution:
Given length of rectangular shaped wire = 40cm
Breadth of rectangular shaped wire = 22cm
Perimeter of the rectangle = 2(Length + Breadth)
= 2(40 cm + 22 cm)
= 124 cm
It is given that the wire which was in the shape of a rectangle is now bent into a square.
Therefore, the perimeter of the square = Perimeter of the rectangle
Perimeter of the square = 124 cm
We know that perimeter of square = 4 x side
Therefore 4 x side = 124 cm
Side = 124/4 = 31 cm
We know that area of rectangle = length x breadth
Now, Area of the rectangle
= 40 cm x 22 cm
= 880 cm
2
We know that area of the square = (Side)
2
= (31 cm)
2
= 961 cm
2
.
Therefore, the square-shaped wire encloses more area.
8. How many square meters of glass will be required for a window, which has 12
panes, each pane measuring 25 cm by 16 cm?
Solution:
Given length of the glass pane = 25 cm
Breadth of the glass pane = 16 cm
We know that area of rectangle = length x breadth
Area of one glass pane = 25 cm x 16 cm
= 400 cm
2
= 0.04 m
2
[Since 1 m
2
= 10000 cm
2
]
Thus, Area of 12 panes = 12 x 0.04 = 0.48 m
2
9. A marble tile measures 10 cm x 12 cm. How many tiles will be required to cover a
wall of size 3 m x 4 m? Also, find the total cost of the tiles at the rate of Rs 2 per tile.
Solution:
Given area of the wall = 3 m x 4 m
= 12 m
2
Also given that area of one marble tile = 10 cm x 12 cm
= 120 cm
2
= 0.012 m
2
[Since 1 m
2
= 10000 c m
2
]
Page 5
1. Find the area, in square metres, of a rectangle whose
(i) Length = 5.5 m, breadth = 2.4 m
(ii) Length = 180 cm, breadth = 150 cm
Solution:
(i) Given Length = 5.5 m, Breadth = 2.4 m
We know that area of rectangle = Length x Breadth
= 5.5 m x 2.4 m = 13.2 m
2
(ii) Given Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [Since 100 cm = 1 m]
We know that area of rectangle = Length x Breadth
= 1.8 m x 1.5 m = 2.7 m
2
2. Find the area, in square centimetres, of a square whose side is
(i) 2.6 cm
(ii) 1.2 dm
Solution:
(i) Given side of the square = 2.6 cm
We know that area of the square = (Side)
2
= (2.6 cm)
2
= 6.76 cm
2
(ii) Given side of the square = 1.2 dm
= 1.2 x 10 cm = 12 cm [Since 1 dm = 10 cm]
We know that area of the square = (Side)
2
= (12 cm)
2
= 144 cm
2
3. Find in square meters, the area of a square of side 16.5 dam.
Solution:
Given side of the square = 16.5
dam = 16.5 x 10 m = 165 m [Since 1 dam/dm (decametre) = 10 m]
Area of the square = (Side)
2
= (165 m)
2
= 27225 m
2
4. Find the area of a rectangular field in acres whose sides are:
(1) 200 m and 125 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 200 m
Breadth of the rectangular field = 125 m
We know that area of the rectangular field = Length x Breadth
= 200 m x 125 m
= 25000 m
2
= 250 acres [Since 100 m
2
= 1 acre]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 90.6 acres [Since 100 m
2
= 1 acre]
5. Find the area of a rectangular field in hectares whose sides are:
(i) 125 m and 400 m
(ii) 75 m 5 dm and 120 m
Solution:
(i) Given length of the rectangular field = 125 m
Breadth of the rectangular field = 400 m
We know that the area of the rectangular field = Length x Breadth
= 125 m x 400 m
= 50000 m
2
= 5 hectares [Since 10000 m
2
= 1 hectare]
(ii) Given length of the rectangular field =75 m 5 dm
= (75 + 0.5) m
= 75.5 m [Since 1 dm = 10 cm = 0.1 m]
Breadth of the rectangular field = 120 m
We know that the area of the rectangular field = Length x Breadth
= 75.5 m x 120 m
= 9060 m
2
= 0.906 hectares [Since 10000 m
2
= 1 hectare]
6. A door of dimensions 3 m x 2m is on the wall of dimension 10 m x 10 m. Find the
cost of painting the wall if rate of painting is Rs 2.50 per sq. m.
Solution:
Given length of the door = 3 m
Also given that breadth of the door = 2 m
Side of the wall = 10 m
We know that Area of the square = (Side)
2
Area of the wall = Side x Side = 10 m x 10 m
= 100 m
2
We know that the area of the rectangle = length x breadth
Area of the door = Length x Breadth = 3 m x 2 m = 6 m
Thus, required area of the wall for painting = Area of the wall – Area of the door
= (100 – 6) m
2
= 94 m
2
Rate of painting per square metre = Rs. 2.50
Hence, the cost of painting the wall = Rs. (94 x 2.50) = Rs. 235
7. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the
same wire is bent in the shape of a square, what will be the measure of each side.
Also, find which side encloses more area?
Solution:
Given length of rectangular shaped wire = 40cm
Breadth of rectangular shaped wire = 22cm
Perimeter of the rectangle = 2(Length + Breadth)
= 2(40 cm + 22 cm)
= 124 cm
It is given that the wire which was in the shape of a rectangle is now bent into a square.
Therefore, the perimeter of the square = Perimeter of the rectangle
Perimeter of the square = 124 cm
We know that perimeter of square = 4 x side
Therefore 4 x side = 124 cm
Side = 124/4 = 31 cm
We know that area of rectangle = length x breadth
Now, Area of the rectangle
= 40 cm x 22 cm
= 880 cm
2
We know that area of the square = (Side)
2
= (31 cm)
2
= 961 cm
2
.
Therefore, the square-shaped wire encloses more area.
8. How many square meters of glass will be required for a window, which has 12
panes, each pane measuring 25 cm by 16 cm?
Solution:
Given length of the glass pane = 25 cm
Breadth of the glass pane = 16 cm
We know that area of rectangle = length x breadth
Area of one glass pane = 25 cm x 16 cm
= 400 cm
2
= 0.04 m
2
[Since 1 m
2
= 10000 cm
2
]
Thus, Area of 12 panes = 12 x 0.04 = 0.48 m
2
9. A marble tile measures 10 cm x 12 cm. How many tiles will be required to cover a
wall of size 3 m x 4 m? Also, find the total cost of the tiles at the rate of Rs 2 per tile.
Solution:
Given area of the wall = 3 m x 4 m
= 12 m
2
Also given that area of one marble tile = 10 cm x 12 cm
= 120 cm
2
= 0.012 m
2
[Since 1 m
2
= 10000 c m
2
]
Number of tiles required to cover the wall = Area of wall/ Area of one marble tile
= 12/0.012
= 1000 tiles
Cost of one tile = Rs. 2
Total cost = Number of tiles x Cost of one tile
= Rs. (1000 x 2)
= Rs. 2000
10. A table top is 9 dm 5 cm long 6 dm 5 cm broad. What will be the cost to polish it at
the rate of 20 paise per square centimetre?
Solution:
Given length of the table top = 9 dm 5 cm
= (9 x 10 + 5) cm
= 95 cm [Since 1 dm = 10 cm]
Also given that Breadth of the table top = 6 dm 5 cm
= (6 x 10 + 5) cm
= 65 cm
Area of the table top = Length x Breadth
= (95 cm x 65 cm)
= 6175 c m
2
Rate of polishing per square centimetre = 20 paise = Rs. 0.20 [since 1Rs. = 100 paise]
Total cost to polish table top = (6175 x 0.20)
= Rs. 1235
11. A room is 9.68 m long and 6.2 m wide. Its floor is to be covered with rectangular
tiles of size 22 cm by 10 cm. Find the total cost of the tiles at the rate of Rs 2.50 per
tile.
Solution:
Given length of the floor of the room = 9.68 m
Breadth of the floor of the room = 6.2 m
We know that area of rectangle = length x breadth
Area of the floor = 9.68 m x 6.2 m
= 60.016 m
2
Given that length of the tile = 22 cm
Breadth of the tile = 10 cm
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FAQs on Mensuration – I (Perimeter and Area of Rectilinear Figures Exercise 20.1) RD Sharma Solutions - Mathematics (Maths) Class 7
| 1. What is mensuration? |  |
Ans. Mensuration is a branch of mathematics that deals with the measurement of geometric figures and their parameters such as length, area, volume, and perimeter.
| 2. How is the perimeter of a rectilinear figure calculated? | |
Ans. The perimeter of a rectilinear figure is calculated by adding the lengths of all its sides. For example, if a rectilinear figure has sides of lengths 5 cm, 8 cm, 6 cm, and 10 cm, then its perimeter would be 5 + 8 + 6 + 10 = 29 cm.
| 3. How is the area of a rectilinear figure calculated? | |
Ans. The area of a rectilinear figure is calculated by dividing it into smaller rectangles and triangles and then finding the sum of their individual areas. The formula for finding the area of a rectangle is length × width, and for a triangle, it is 1/2 × base × height.
| 4. Can you provide an example of calculating the area of a rectilinear figure? | |
Ans. Sure! Let's consider a rectilinear figure with sides of lengths 4 cm, 6 cm, 8 cm, and 5 cm. We can divide this figure into rectangles and triangles. By calculating the area of each rectangle and triangle and summing them up, we can find the total area of the figure.
For example, the area of the rectangle with sides 4 cm and 6 cm would be 4 × 6 = 24 square cm. Similarly, the area of the triangle with base 8 cm and height 5 cm would be 1/2 × 8 × 5 = 20 square cm.
Adding up the areas of all the rectangles and triangles, we get the total area of the rectilinear figure.
| 5. What is the importance of learning mensuration? | |
Ans. Learning mensuration is important as it helps in real-life applications such as calculating the area of a field, finding the perimeter of a room, measuring the volume of a container, etc. It also enhances our spatial reasoning, problem-solving skills, and mathematical understanding. Mensuration is widely used in various fields like architecture, engineering, construction, and design.
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RD Sharma Solutions: Mensuration – I (Perimeter and Area of Rectilinear Figures Exercise 20.1) Notes
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RD Sharma Solutions: Mensuration – I (Perimeter and Area of Rectilinear Figures Exercise 20.1) Class 7 Questions
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