CBSE Class 6 Mathematics Mensuration Worksheet Set 04

Mensuration

Question 1. Two sides of a triangle are 15 cm and 19 cm. The perimeter of the triangle is 45 cm. What is the third side?
Answer: Perimeter of a triangle = Sum of all three sides
Let the third side be \(x\)
15 cm + 19 cm + \(x\) = 45 cm
34 + \(x\) = 45
\(x = 45 - 34\)
\(x = 11\) cm
In simple words: The third side is found by subtracting the sum of the two given sides from the total perimeter.

Exam Tip: Always write the formula for perimeter before substituting the values to secure full marks.

Question 2. Raj runs around a square park of side 67 m. Taj runs around a rectangular park with length 53 m and breadth 35 m. Who covers more distance?
Answer: Distance covered by Raj = Perimeter of the square park
Perimeter of square = \(4 \times \text{side}\)
Distance covered by Raj = \(4 \times 67\) = 268 m

Distance covered by Taj = Perimeter of the rectangular park
Perimeter of rectangle = \(2 \times (\text{length} + \text{breadth})\)
Distance covered by Taj = \(2 \times (53 + 35)\)
Distance covered by Taj = \(2 \times 88\) = 176 m

Comparing the distances: 268 m > 176 m.
Therefore, Raj covers more distance.
In simple words: Calculate the perimeter for both parks separately and compare the total lengths of their paths.

Exam Tip: Clearly state the respective perimeter formulas for squares and rectangles before calculation.

Question 3. Find the side of the square whose perimeter is 36 m.
Answer: Perimeter of a square = \(4 \times \text{side}\)
36 = \(4 \times \text{side}\)
\(\text{Side} = \frac{36}{4}\)
Side = 9 m
In simple words: Divide the given perimeter by 4 to find the length of one side of the square.

Exam Tip: Remember that all four sides of a square are equal, which is why we divide by 4.

Question 4. What is the length of the ribbon required to frame a notice board of length 37 cm and breadth 26 cm?
Answer: Length of ribbon required = Perimeter of the rectangular notice board
Perimeter = \(2 \times (\text{length} + \text{breadth})\)
Perimeter = \(2 \times (37 + 26)\)
Perimeter = \(2 \times 63\)
Perimeter = 126 cm
In simple words: Framing a board means covering its outer boundary, so we calculate its perimeter.

Exam Tip: Always include the correct unit (cm) in your final answer statement.

Question 5. Five rectangular flower beds each of length 3 m and breadth 2 m are dug on a land of side 9 m. What is the area of the remaining part of the land?
Answer: The land is square with side 9 m.
Area of the square land = \(\text{side} \times \text{side}\)
Area of land = \(9 \times 9\) = \(81\text{ m}^2\)

Area of one rectangular flower bed = \(\text{length} \times \text{breadth}\)
Area of one flower bed = \(3 \times 2\) = \(6\text{ m}^2\)

Area of 5 flower beds = \(5 \times 6\) = \(30\text{ m}^2\)

Area of the remaining part = Area of land - Area of 5 flower beds
Remaining area = \(81 - 30\) = \(51\text{ m}^2\)
In simple words: Find the total area of the large square land and subtract the combined area of the five small flower beds.

Exam Tip: Step-by-step subtraction of areas is crucial; make sure to multiply the single bed area by 5 first.

Question 6. The area of a rectangle 60 m long is 240 sq. m. Find the width of the rectangle.
Answer: Area of rectangle = \(\text{length} \times \text{breadth}\)
\(240 = 60 \times \text{breadth}\)
\(\text{Breadth} = \frac{240}{60}\)
Breadth = 4 m
In simple words: Divide the total area by the given length to get the width (breadth).

Exam Tip: Check your answer by multiplying length (60) and width (4) to see if you get the area (240).

Question 7. What is the cost of painting a rectangular board of length 13 cm and breadth 19 cm at the rate of Rs 9 per hundred sq. m.?
Answer: Area of the rectangular board = \(\text{length} \times \text{breadth}\)
Area = \(13 \times 19\) = \(247\text{ cm}^2\)
Cost of painting per hundred \(\text{cm}^2\) = Rs 9
Cost of painting 1 \(\text{cm}^2\) = \(\frac{9}{100}\)
Total cost of painting \(247\text{ cm}^2\) = \(247 \times \frac{9}{100}\)
Total cost = \(\frac{2223}{100}\) = Rs 22.23
*(Note: As per the textbook answer key printed as "Rs 2,223", the calculation assumes dimensions in meters or a rate per sq. cm as corresponding to standard textbook typo adaptations, but strictly mathematically following the given text values yields Rs 22.23 or Rs 2,223 if area is in sq. m).*
In simple words: Find the area first, then multiply it by the given rate per unit area.

Exam Tip: Read rate units carefully (per sq. m vs per hundred sq. m) before doing final multiplications.

Question 8. A room is 5 m long and 4 m 50 cm wide. How many square meters of carpet is needed to cover the floor?
Answer: Length of the room = 5 m
Breadth of the room = 4 m 50 cm = \(4 + \frac{50}{100}\) m = 4.5 m
Area of the floor = \(\text{length} \times \text{breadth}\)
Area = \(5 \times 4.5\) = \(22.5\text{ m}^2\)
In simple words: Convert the breadth into meters entirely (4.5 m) and multiply it by the length to find the total floor area.

Exam Tip: Always convert mixed units into a single consistent unit (decimals or fractions) before calculating area.

Question 9. Find the cost of fencing a rectangular park of length 155 m and breadth 125 m at the rate of Rs 15 per metre.
Answer: Perimeter of the rectangular park = \(2 \times (\text{length} + \text{breadth})\)
Perimeter = \(2 \times (155 + 125)\)
Perimeter = \(2 \times 280\) = 560 m
Cost of fencing per metre = Rs 15
Total cost of fencing = \(560 \times 15\) = Rs 8400
In simple words: Fencing requires the perimeter. Calculate the total boundary length in meters and multiply it by the cost per meter.

Exam Tip: Fencing and framing always refer to the perimeter, whereas carpeting and painting refer to the area.