CBSE Class 6 Mathematics Mensuration Worksheet Set 01

1. Fill in the blanks.

Question 1(i). Distance covered along the boundary of a close figure _________________.
Answer: perimeter
In simple words: The total length of the outer boundary of a closed shape is called its perimeter.
Exam Tip: Remember that perimeter is always a linear measurement (units like cm, m, km).

Question 1(ii). Perimeter of a rectangle is =
Answer: \(2 \times (\text{length} + \text{breadth})\)
In simple words: Add the length and breadth together and multiply the sum by 2 to get the perimeter of a rectangle.

Exam Tip: Always write the formula clearly before substituting the given values.

Question 1(iii). Area of a square =
Answer: \(\text{side} \times \text{side}\) (or \(\text{side}^2\))
In simple words: Multiply the length of one side of a square by itself to find its area.

Exam Tip: Area is always expressed in square units (like \(\text{cm}^2\) or \(\text{m}^2\)).

Question 1(iv). Perimeter of an equilateral triangle =
Answer: \(3 \times \text{side}\)
In simple words: Since all 3 sides of an equilateral triangle are equal, multiply the length of one side by 3.

Question 1(v). 1 cm = _________ mm
Answer: 10
In simple words: One centimetre is equal to 10 millimetres.

Exam Tip: To convert cm to mm, multiply by 10.

Question 1(vi). 1 kilometer = ____________ metre
Answer: 1000
In simple words: One kilometre is equal to 1000 metres.

Exam Tip: The prefix 'kilo-' always means one thousand times.

2. MCQ

Question 2(i). The amaint of surface enclosed by a close figure is
(a) Volume
(b) area
(c) side
(d) perimeter
Answer: (b) area
The measure of the region enclosed by a closed plane figure is called its area.
In simple words: The flat space inside a closed shape is its area.

Exam Tip: Do not confuse area (surface inside) with perimeter (boundary distance).

Question 2(ii). One square meter = ____________ square cm.
(a) 100
(b) 1000
(c) 10000
(d) 10
Answer: (c) 10000
Since \(1\text{ m} = 100\text{ cm}\),
\(1\text{ m}^2 = 1\text{ m} \times 1\text{ m} = 100\text{ cm} \times 100\text{ cm} = 10000\text{ cm}^2\).
In simple words: 1 square metre is 100 cm by 100 cm, which equals 10,000 square centimetres.

Exam Tip: When converting square units, square the conversion factor (e.g., \(100^2 = 10000\)).

Question 2(iii). ___________ is measured in square units.
(a) Perimeter
(b) area
(c) side
(d) Volume
Answer: (b) area
Area represents two-dimensional surface coverage, hence measured in square units.
In simple words: Areas are always measured in square units like square cm or square metres.

Exam Tip: Volume is measured in cubic units, and perimeter in linear units.

3. Solve :-

Question 3(i). Find the perimeter of the figure.
Answer:
The given figure is a pentagon with side lengths \(2\text{ cm}\), \(2\text{ cm}\), \(2\text{ cm}\), \(2\text{ cm}\), and \(2\text{ cm}\).
Perimeter = Sum of all outer sides
Perimeter = \(2\text{ cm} + 2\text{ cm} + 2\text{ cm} + 2\text{ cm} + 2\text{ cm} = 10\text{ cm}\)
In simple words: Add all the outer side lengths together to find the total perimeter.

Exam Tip: Make sure to count all outer edges of the figure and do not include any internal lines.

Question 3(ii). Find the area in square meter of a piece of cloth, 5m long and 2m wide.
Answer:
Length of the cloth \((l) = 5\text{ m}\)
Breadth of the cloth \((b) = 2\text{ m}\)
Area of the rectangular cloth = \(l \times b\)
Area = \(5\text{ m} \times 2\text{ m} = 10\text{ m}^2\)
In simple words: Multiply the length by the breadth to get the area in square metres.

Exam Tip: Check that both dimensions are in the same units before calculating the area.

Question 3(iii). By counting the squares, estimate the area of the figure
Answer:
Looking at the grid with vertices labeled A, B, C, D:
- Count the number of fully filled squares inside the boundary: 4 full squares.
- Count the number of half-filled or partially filled squares and estimate their combined area as equivalent to 2 full squares.
Estimated Area = \(4 + 2 = 6\text{ square units}\).
In simple words: Count the full squares as 1 and half squares as 0.5 (or combine them) to estimate the total area.

Exam Tip: When estimating area on a grid, count fully filled squares first, then combine half-filled squares.

Question 3(iv). A rectangular hall is of length 14m & breadth 12m. How many square tiles of side 10cm are need to cover the floor of the hall.
Answer:
Length of the hall \((L) = 14\text{ m} = 14 \times 100\text{ cm} = 1400\text{ cm}\)
Breadth of the hall \((B) = 12\text{ m} = 12 \times 100\text{ cm} = 1200\text{ cm}\)
Area of the hall = \(L \times B = 1400\text{ cm} \times 1200\text{ cm} = 1,680,000\text{ cm}^2\)
Side of one square tile \((s) = 10\text{ cm}\)
Area of one square tile = \(s \times s = 10\text{ cm} \times 10\text{ cm} = 100\text{ cm}^2\)
Number of tiles required = \(\frac{\text{Area of the hall}}{\text{Area of one tile}}\)
Number of tiles = \(\frac{1680000}{100} = 16,800\)
In simple words: Convert the hall dimensions into centimetres, find the area of the hall and one tile, then divide the total area by the tile area.

Exam Tip: Always convert all dimensions to the same unit (metres to centimetres) before calculating areas and division.

Choose the correct option in question 1,2,3 and 4

Q.1 Breadth of rectangle = ________ perimeter – 1
(a) 2
(b) ½
(c) 1
(d) none

Q.2 In which of the following perimeter is not used?
(a) framing a photo
(b) sowing seeds in a field
(c) fencing a field
(d) building a boundary wall of a house.

Q.3 If length of rectangle is doubled and breadth is halved, then the new area becomes
(a) double
(b) four times
(c) remains the same
(d) none of these

Q.4 The perimeter of a rectangle of an area 650 cm2 whose breadth is 13 cm is _____
(a) 112 cm
(b) 122cm
(c) 126 cm
(d) none

Q.5 The length of a rectangular field is 100m. If its perimeter is 300, what is its breadth?

Q.6 A square piece of land has each side equal to 100m. If 3 layers of metal wire have to be used to fence it, what is the length of the wire needed?

Q.7 Find the cost of fencing a rectangular park of length 175m and breadth 125m at the rate of Rs. 12 per metre.

Q.8 The perimeter of a regular pentagon is 100 cm. How long is each side?

Q.9 A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with four rows of wires. What is the length of the wire needed?

Q.10 Find the side of a square whose perimeter is 90 cm.

Q.11 Find the perimeter of a regular octagon with side 12.8 cm.

Q.12 Find the side of a regular hexagon with perimeter 84 cm.

Q.13 The area of a rectangle is 225 cm2 and its one side is 25 cm. Find its other side

Q.14 A rectangle has the area equal to that of a square of side 80cm. If the breadth of the rectangle is 20 cm, find its length.

Q.15 Area of a rectangle of breadth 17cm is 340 cm2. Find the perimeter of the rectangle.

Q.16 A marble tile measures 10 cm × 12 cm. How many tiles will be required to cover a wall of size 3m × 4m? Also, find the total cost of the tiles at the rate of Rs. 2 per tile.

Q.17 Find the cost of levelling a playground at Rs. 5 per square metre if it is 28m long and 16m wide. Also, find the cost of fencing it at Rs. 2.40 per metre.

Q.18 Bhola and Raju bought one field each with dimensions 50m by 40m and  100m by 30m. They purchased the land at the rate of Rs. 500 per square metre. Who paid more and by how much?

Q.19 How long will it take a boy to go around a regular pentagon of side 7m, at a speed of 5m per minute.

Q.20 Sujit painted a wall of 45m by 30m and the money he got for his work was Rs.20 for per square m.How much money he made. He always gives half of his income to orphanage. Calculate how much money he gave to the orphanage. What value you learn from Sujit?

1. The length and breadth of a Rectangle are 11 cm and 9 cm.
Find its area and Perimeter ?

2. The area of a Rectangle is 144 sq cm and its length is 16 cm. Find the breadth of the Rectangle?

3. Find the perimeter of a regular hexagon of side x cm.

4. If the perimeter of a regular pentagon is 65 cm. Find its side ?

5. The perimeter of a triangle is 42 cm. If two of its sides are 16 cm and 12 cm. Find its third side?

6. A piece of string is 45 cm long. It is bent to form an equilateral triangle. Find the side of triangle.

7. An athlete takes 5 rounds of a rectangular park 120 m long and 80m wide. Find the total distance covered by him.

8. Find the area of a square whose perimeter is 260 cm.

9. The total cost of fencing a square park at Rs. 20 per metre is Rs. 2880. Find the side of the square park.

10. The floor of a room with dimensions 5 m and 3m is to be covered with square tiles. If each square tile is of side 25 cm. Find the number of tiles required.