## NCERT Solutions for Class 6 Maths Chapter - 10: Mensuration## Exercise 10.1
(a)
Perimeter = 4 cm + 2 cm + 1 cm + 5 cm Perimeter = 12 cm (b)
Perimeter = 35 cm + 23 cm + 35 cm + 40 cm Perimeter = 133 cm (c)
Perimeter = 15 cm + 15 cm + 15 cm + 15 cm Perimeter =60 cm (d)
Perimeter = 4 cm + 4 cm + 4 cm + 4 cm + 4 cm Perimeter = 40 cm (e)
Perimeter = 4 cm + 4 cm + 1 cm + 0.5 cm + 0.5 cm + 2.5 cm + 2.5 cm Perimeter = 15 cm (f)
Here, the four parts of the given have the same dimensions. So, we will find the sum of the first part and multiply it with 4. Perimeter = 4 � (4 cm + 3 cm + 3 cm + 2 cm + 1 cm) = 4 � 13 cm = 52 cm Or We can randomly calculate the total sum of the length of the sides of the given figure. Perimeter = 4 cm + 3 cm + 3 cm + 2 cm + 1 cm + 4 cm + 3 cm + 3 cm + 2 cm + 1 cm + 4 cm + 3 cm + 3 cm + 2 cm + 1 cm + 4 cm + 3 cm + 3 cm + 2 cm + 1 cm Perimeter = 52 cm
Sum of the length of all sides of a given figure is known as perimeter. Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (40 + 10) = 2 � 50 = 100 cm Thus, the length of the tape required will be 100 cm. 1 m = 100 cm So, we can also say that the length of the tape required will be 1 m.
Sum of the length of all sides of a given figure is known as perimeter. Perimeter of a rectangle = 2 � (Length + Breadth) 2 m 25 cm = 2.25 m (1 m = 100 cm) 1m 50 cm = 1.50 m Perimeter = 2 � (2.25 + 1.50) = 2 � 3.75 = 7.50 m Thus, the perimeter of the table top is 7.5 m or 7 m 50 cm.
Breadth = 21 cm Length of the wooden strip = Sum of length of all sides of the rectangular frame Sum of the length of all sides of a given figure is known as perimeter. Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (32 + 21) = 2 � 53 = 106 cm Thus, the length of the wooden strip required framing a photograph of length and breadth 32 cm and 21 cm is
Breadth = 0.5 km Length of the rectangular piece of land = Sum of length of all sides of the rectangular land Sum of the length of all sides of a given figure is known as perimeter. Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (0.7 + 0.5) = 2 � 1.2 = 2.4 km The length required by the land to be fenced with 1 row of wire = 2.4 km The length required by the land to be fenced with 4 rows of wire = 2.4 km � 4 =
Perimeter of a triangle = 3 cm + 4 cm + 5 cm = 12 cm
Perimeter of an equilateral triangle = 3 � (Side) It is because all the sides of an equilateral triangle are equal. Perimeter of an equilateral triangle = 3 � 9 = 27 cm
Perimeter of an = 22 cm
Perimeter of a triangle = 10 cm + 14 cm + 15 cm = 39 cm
A hexagon has six sides. Perimeter of the hexagon = 6 � (Side) It is because all the sides of a hexagon are equal. Perimeter of the hexagon = 6 � 8 = 48 m
A square has four sides. Perimeter of the square = 4 � (Side) It is because all the sides of a square are equal. 20 m = 4 � (Side) Side = 20/4 Side = 5 m Thus, the side of the square of perimeter 20 is
A pentagon has five sides. Perimeter of the pentagon = 5 � (Side) It is because all the sides of a pentagon are equal. 100 cm = 5 � (Side) Side = 100/5 Side = 20 cm Thus, the side of the pentagon of perimeter 100 is
A square has four sides. Perimeter of the square = 4 � (Side) It is because all the sides of a square are equal. 30 cm = 4 � (Side) (Side) = 30/4 (Side) = 7.5 cm Thus, the length of each side of a square is 7.5 cm.
An equilateral triangle has three sides. Perimeter of the equilateral triangle = 3 � (Side) It is because all the sides of the equilateral triangle are equal. 30 cm = 3 � (Side) (Side) = 30/3 (Side) = 10 cm Thus, the length of each side of an equilateral triangle is 10 cm.
A hexagon triangle has six sides. Perimeter of the hexagon = 6 � (Side) It is because all the sides of the hexagon are equal. 30 cm = 6 � (Side) (Side) = 30/6 (Side) = 5 cm Thus, the length of each side of the hexagon is 5 cm.
Perimeter of a triangle = Length of the first side + Length of the second side + Length of the third side 36 = 12 + 14 + Length of the third side 36 = 26 + Length of the third side Length of the third side = 36 - 26 = 10 cm Thus, the length of the third side of the triangle is 10 cm.
Perimeter of the square = 4 � (Side) It is because all the sides of a square are equal. Perimeter = 4 � 250 = 1000 m Cost of fencing a square park = Perimeter � Cost per meter = 1000 � 20 = 20000 Thus, the cost of fencing a square park at the rate of rupees 20 per meter is
Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (175 + 125) = 2 � 300 = 600 m Cost of fencing a rectangular park = Perimeter � Cost per meter = 600 � 12 = 7200 Thus, the cost of fencing a rectangular park at the rate of rupees 12 per meter is
Length of a rectangular park = 60 m Breadth of a rectangular park = 45m Perimeter of a square = 4 � (Side) Perimeter of a square = 4 � 75 = 300 m Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (60 + 45) Perimeter = 2 � 105 = 210 m Perimeter of a rectangle < Perimeter of a square Thus, Bulbul covers less distance.
Sum of the length of all sides of a given figure is known as perimeter. Perimeter of a square = 4 � (Side) Perimeter of a square = 4 � 25 = 100 cm (b)
Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (40 + 10) Perimeter = 2 � 50 = 100 cm (c)
Perimeter of a rectangle = 2 � (Length + Breadth) Perimeter = 2 � (20 + 30) Perimeter = 2 � 50 = 100 cm (d)
Perimeter of a triangle = Sum of all the three sides Perimeter = 30 + 30 + 40 = 100 cm Here, we
All the four sides of the above figure are equal, hence it is a square. Each sides has thee slabs. Length of each side = 1/2m +1/2m +1/2m = 3/2 m Perimeter of a square = 4 � (Side) Perimeter of a square = 4 � 3/2 = 6 m
There are total four crosses in the given figure. Each cross has five slabs. = � + � + � + � + � = 5/2 Perimeter of 1 cross = 5/2 m Perimeter of four crosses =4 � 5/2 m = 10 m Thus, the perimeter of the given cross figure is 10 m.
## Exercise 10.2
Area of 1 square = 1 sq units Area of half square = � sq units Area of more than half filled square = 1 sq units (approx.) Area of less than half filled square = 0 sq units (approx.) (a)
Area = Number of square x Area of 1 square Area = 9 � 1 sq unit Area = 9 sq units (b)
Area = Number of square x Area of 1 square Area = 5 � 1 sq unit Area = 5 sq units (c)
Number of full squares = 2 Area of full square = 2 � 1 sq unit = 2 sq units Number of half squares = 4 Area of half square = 4 � 1/2 sq unit = 2 sq units Total area = Area of full squares + area of half squares Total area = 2 sq units + 2 sq units Total area = 4 sq units (d)
Area = Number of square x Area of 1 square Area = 8 � 1 sq unit Area = 8 sq units (e)
Area = Number of squares x Area of 1 square Area = 10 � 1 sq unit Area = 10 sq units (f)
Number of full squares = 2 Area of full square = 2 � 1 sq unit = 2 sq units Number of half squares = 4 Area of half square = 4 � 1/2 sq unit = 2 sq units Total area = Area of full squares + area of half squares Total area = 2 sq units + 2 sq units Total area = 4 sq units (g)
Number of full squares = 4 Area of full square = 4 � 1 sq unit = 4 sq units Number of half squares = 4 Area of half square = 4 � 1/2 sq unit = 2 sq units Total area = Area of full squares + area of half squares Total area = 4 sq units + 2 sq units Total area = 6 sq units (h)
Area = Number of squares x Area of 1 square Area = 5 � 1 sq unit Area = 5 sq units (i)
Area = Number of squares x Area of 1 square Area = 9 � 1 sq unit Area = 9 sq units (j)
Number of full squares = 2 Area of full square = 2 � 1 sq unit = 2 sq units Number of half squares = 4 Area of half square = 4 � 1/2 sq unit = 2 sq units Total area = Area of full squares + area of half squares Total area = 2 sq units + 2 sq units Total area = 4 sq units (k)
Number of full squares = 4 Area of full square = 4 � 1 sq unit = 4 sq units Number of half squares = 2 Area of half square = 2 � 1/2 sq unit = 1 sq unit Total area = Area of full squares + area of half squares Total area = 4 sq units + 1 sq units Total area =5 sq units (l)
Number of full squares = 2 Area of full square = 4 � 1 sq unit = Number of half-filled squares = 0 Number of more than half filled squares = 6 Area of 1 more than half filled square is considered as 1 sq unit. Area of more than half filled squares = 6 � 1 sq unit = Number of less than half filled squares = 6 Area of 1 less than half filled square is considered as 0 sq units. Area of more than half filled squares = 6 � 0 sq unit = Total area = Area of full squares + area of more than half filled squares + area of less than half filled squares Total area = 2 sq units + 6 sq units + 0 sq units Total area = (m)
Here, there are full, less than half filled squares, and more than half filled squares. Number of full squares = 5 Area of full square = 5 � 1 sq unit = Number of half-filled squares = 0 Number of more than half filled squares = 9 Area of more than half filled squares = 9 � 1 sq unit = Number of less than half filled squares = 12 Area of 1 less than half filled square is considered as 0 sq units. Area of more than half filled squares = 12 � 0 sq unit = Total area = Area of full squares + area of more than half filled squares + area of less than half filled squares Total area = 5 sq units + 9 sq units + 0 sq units Total area = (n)
Here, there are full, less than half filled squares, and more than half filled squares. Number of full squares = 9 Area of full square = 9 � 1 sq unit = Number of half-filled squares = 0 Number of more than half filled squares = 9 Area of 1 more than half filled square is considered as 1 sq unit. Area of more than half filled squares = 9 � 1 sq unit = Number of less than half filled squares = 10 Area of 1 less than half filled square is considered as 0 sq units. Area of more than half filled squares = 10 � 0 sq unit = Total area = Area of full squares + area of more than half filled squares + area of less than half filled squares Total area = 9 sq units + 9 sq units + 0 sq units Total area = ## Exercise 10.3
Area of rectangle = 3 cm � 4 cm = 12 sq cm
Area of rectangle = 12 m � 21 m Area of rectangle = 252 sq m
Area of rectangle = 2 km � 3 km Area of rectangle = 6 sq km
Length = 2m Breadth = 70 cm Since the length and breadth are present in different units, we need to convert it into the same units. 1m = 100 cm Breadth = 0.7 m Area of rectangle = 2 m � 0.7 m = 1.4 sq m
Area of square = 10 cm � 10 cm Area of square = 100 sq cm
Area of square = 14 cm � 14 cm Area of square = 196 sq cm
Area of square = 5 m � 5 m Area of square = 25 sq m
Area of rectangle = 9 m � 6 m Area of rectangle = 54 sq m
Area of rectangle = 17 m � 3 m Area of rectangle = 51 sq m
Area of rectangle = 4 m � 14 m Area of rectangle = 56 sq m
Length of the rectangular garden = 50 m Area of rectangle = Length � Width 300 sq m = 50 m � Width Width = 300/50 Width = 6 m Thus, the width of the rectangular garden is 6m.
Width of a rectangular plot = 200 m Area = Length � Width Area = 500 � 200 Area = 100000 sq m Cost of tiling a rectangular plot = Area � Rate per square meter Cost of tiling a rectangular plot per square meter = 100000 sq m � 8 rupees = 800000 Cost of tiling a rectangular plot per hundred square meter = 800000/100 = Rupees 8,000
Width of the table top = 1m 50 cm = 1.5 m Area of the table top = Length � Width Area of the table top = 2m � 1.5 m Area of the table top = 3 sq m
Width of the room = 3m 50 cm = 3.5 m Area of the room = Length � Width Area of the room = 4m � 3.5 m Area of the room = 14 sq m Thus, 14 square metres of carpet are needed to cover the floor of the room.
Width of the floor = 4m Area of the floor = Length � Width Area of the floor = 5m � 4m
Side of the square carpet = 3m Area of square = Side � Side Area of square = 3 m � 3 m
Area of the floor not carpeted = Total area of the floor - carpeted area Area of the floor not carpeted = 20 - 9 =
Width of the land = 4m Area of the land = Length � Width Area of the land = 5m � 4m
Side of the square bed = 1m Area of square = Side � Side Area of square bed = 1 m � 1 m Area of square bed = 1 sq m
Area of the remaining part of the land = Total area - Area of 5 square beds = 20 - 5 =
Total area = Area of rectangle a + Area of rectangle b + Area of rectangle c + Area of rectangle d Total area = 1 � 2 + 2 � 5 + 1 � 7 + 3 � 3 Total area = 2 sq cm + 10 sq cm + 7 sq cm + 9 sq cm Total area = 28 sq cm
Total area = Area of rectangle a + Area of rectangle b + Area of rectangle c Total area = 5 � 1 + 2 � 1 + 1 � 2 Total area = 5 sq cm + 2 sq cm + 2 sq cm Total area = 9 sq cm
Total area = Area of rectangle a + Area of rectangle b Total area = 12 � 2 + 2 � 8 Total area = 24 sq cm + 16 sq cm Total area = 40 sq cm
Length of rectangle b = (7 + 7 + 7) = 21 cm Total area = Area of rectangle a + Area of rectangle b + Area of rectangle c Total area = 7 � 7 + 21 � 7 + 7 � 7 Total area = 49 sq cm + 147 sq cm + 49 sq cm Total area = 245 sq cm
Total area = Area of rectangle a + Area of rectangle b Total area = 5 � 1 + 4 � 1 Total area = 5 sq cm + 4 sq cm Total area = 9 sq cm
Area of tile = 12 cm � 5 cm Area of tile = 60 sq cm
Width of the rectangular region = 144 cm Area of the rectangular region = Length � Width Area of the rectangular region = 100 � 144 = 14400 sq cm Area of tile = 60 sq cm Number of tiles needed to fit into the rectangular region = Area of rectangular region/Area of tile = 14400/60 = 240 Thus, 240 numbers of tiles are required to fit into the rectangular region.
Width of the rectangular region = 36 cm Area of the rectangular region = Length � Width Area of the rectangular region = 70 � 36 = 2520 sq cm Area of tile = 60 sq cm Number of tiles needed to fit into the rectangular region = Area of rectangular region/Area of tile = 2520/60 = 42 Thus, 42 numbers of tiles are required to fit into the rectangular region. Next TopicClass 6 Maths Chapter 11 |