Important Questions Test: Mensuration - Class 6 MCQ

Given information:
- The perimeter of a square is 100 cm.
To find:
- The length of one side of the square.
Let's assume that the length of one side of the square is 's' cm.
Perimeter of a square:
The perimeter of a square is the sum of the lengths of all its sides.
In this case, the perimeter is given as 100 cm. So,
Perimeter of the square = 4 * side length
Substituting the given values, we get:
100 cm = 4 * s cm
Now, let's solve for the side length 's':
100 cm = 4s cm
Dividing both sides of the equation by 4, we get:
25 cm = s cm
Therefore, the length of one side of the square is 25 cm.
Answer: B. 25 cm

Given information:
- The perimeter of a square is 44 cm.
To find:
- The area of the square.
Step 1: Understanding the problem
- We are given the perimeter of a square, which is the sum of all four sides of the square.
- The formula for the perimeter of a square is P = 4s, where P represents the perimeter and s represents the length of one side of the square.
- We need to find the area of the square.
Step 2: Using the given information to find the length of one side of the square
- Since the perimeter of the square is 44 cm and the formula for the perimeter of a square is P = 4s, we can set up the equation 44 = 4s.
- Solving for s, we divide both sides of the equation by 4: s = 44/4 = 11 cm.
- Therefore, the length of one side of the square is 11 cm.
Step 3: Finding the area of the square
- The formula for the area of a square is A = s^2, where A represents the area and s represents the length of one side of the square.
- Substituting the value of s into the formula, we get A = (11 cm)^2 = 121 cm^2.
Step 4: Final Answer
- The area of the square is 121 cm^2. Therefore, the correct answer is option A.

Given: Perimeter of the square = 16 cm
To find: Area of the square
Let's assume that the length of one side of the square is 's'.
Step 1: Find the length of one side of the square
Perimeter of a square = 4 * s
Given that the perimeter is 16 cm, we can write the equation as:
4s = 16
Divide both sides by 4:
s = 16 / 4
s = 4 cm
Therefore, the length of one side of the square is 4 cm.
Step 2: Find the area of the square
Area of a square = s * s
Substitute the value of 's' we found earlier:
Area = 4 cm * 4 cm
Area = 16 cm²
Therefore, the area of the square is 16 cm².
Answer: A) 16 cm²

Given:
- The side of the square is 8 cm.
To find:
- The new perimeter when the side is doubled.
Calculation:
1. The perimeter of a square is given by the formula: P = 4s, where s is the length of a side.
2. The given square has a side length of 8 cm, so its initial perimeter is P = 4(8) = 32 cm.
3. When the side length is doubled, the new side length becomes 2 * 8 = 16 cm.
4. The new perimeter is then given by P = 4(16) = 64 cm.
Answer:
The new perimeter of the square, when its side is doubled, is 64 cm. Therefore, the correct answer is option D.

We are given that the length of the rectangle is 10 cm and the breadth is 8 cm.

Step 1: Calculate the area of the rectangle using the formula: Area = Length × Breadth.

• Area = 10 cm × 8 cm = 80 cm².

Step 2: Double the length of the rectangle.

• New length = 2 × 10 cm = 20 cm.

Step 3: Calculate the new area of the rectangle using the formula: Area = Length × Breadth.

• New area = 20 cm × 8 cm = 160 cm².

Therefore, the new area of the rectangle is 160 cm².

Final Answer: C. 160 cm².

Area of a rectangle = length × breadth
To calculate the area of a rectangle, you need to multiply its length by its breadth. Here's a step-by-step explanation:
1. Identify the length and breadth: The length is the measurement of the longer side of the rectangle, and the breadth is the measurement of the shorter side.
2. Multiply the length and breadth: Once you have identified the length and breadth, multiply them together. This will give you the product of the two measurements.
3. Result: The result of the multiplication is the area of the rectangle. It is expressed in square units since it represents the amount of space inside the rectangle.
For example, if the length of a rectangle is 5 units and the breadth is 3 units, the area would be calculated as follows:
Area = length × breadth
= 5 units × 3 units
= 15 square units
So, the area of the rectangle is 15 square units.
Summary:
- The formula to calculate the area of a rectangle is length × breadth.
- The area represents the amount of space inside the rectangle and is expressed in square units.
- To find the area, multiply the length and breadth together.
- It is important to correctly identify the length and breadth of the rectangle before performing the calculation.

Side of Square = a²

(7)²

= 49 m²

Perimeter
The perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once. It is the sum of all the lengths of the sides of the figure.
Explanation:
- When we measure the perimeter of a figure, we are essentially measuring the distance around the figure.
- Perimeter is a one-dimensional measurement, as it only considers the lengths of the sides of the figure.
- It is important to note that the perimeter is dependent on the shape and size of the figure. Different figures will have different perimeters even if they have the same area.
- To calculate the perimeter of a figure, we add up the lengths of all the sides. For example, in the case of a rectangle, we add the lengths of all four sides.
- The perimeter is commonly used in real-life applications such as measuring the length of a fence, determining the amount of material needed for the boundary of a garden, or calculating the distance around a track.
In conclusion, the distance covered along the boundary forming a closed figure when you go round the figure once is known as the perimeter. It is an important concept in geometry and is used to measure the length or distance around a figure.

To find the perimeter of a square, we need to multiply the length of one side by 4, as all sides of a square are equal in length.
The formula for the perimeter of a square is:
Perimeter = 4 * Length of a side
Step-by-step solution:
1. Identify the formula for the perimeter of a square: Perimeter = 4 * Length of a side.
2. The question states that the length of a side is multiplied by the perimeter to find the perimeter of a square.
3. We need to choose the option that correctly represents the formula for finding the perimeter of a square.
4. Option A: 4. This option correctly represents the formula for the perimeter of a square, as it shows that the perimeter is equal to 4 times the length of a side.
5. Option B: 3. This option does not represent the correct formula for finding the perimeter of a square. It is incorrect.
6. Option C: 2. This option does not represent the correct formula for finding the perimeter of a square. It is incorrect.
7. Option D: None of these. This option does not represent the correct formula for finding the perimeter of a square. It is incorrect.
8. Therefore, the correct answer is option A: 4.
Answer: A. 4

Let ABCD is a park whose lengths are BC, AD and widths are AB, CD, respectively. Hence, AB = CD = 80 m. and BC = DA = 150m Now, the sum of the lengths of four sides 

=AB + BC + CD + DA

= 80 m + 150 m + 80 m + 150 m

= (80 + 150 + 80 + 150) m

=460 m

Perimeter of the park = sum of the lengths of four sides of the park = 460 m

Hence, distance covered by Meera is 460 m.

Step 1: Convert the width measurement to meters
- The width of the room is given as 3 m 50 cm.
- 50 cm is equal to 0.5 m (since there are 100 cm in 1 m).
- So, the width of the room is 3.5 m.
Step 2: Calculate the area of the room
- The area of a rectangle is calculated by multiplying its length and width.
- The length of the room is 4 m and the width is 3.5 m.
- So, the area of the room is 4 m * 3.5 m = 14 m².
Step 3: Determine the amount of carpet needed
- The area of the room represents the amount of carpet needed to cover the floor.
- Therefore, 14 square meters of carpet is required to cover the floor of the room.
Step 4: Choose the correct answer
- Based on the calculations, the correct answer is A: 14 m².

To find the area of a square, we need to know the length of one side of the square.
Let's assume the length of one side of the square is 's'.
Given that the perimeter of the square is 48 cm.
We know that the perimeter of a square is given by the formula:
Perimeter = 4s
Substituting the given value, we have:
48 = 4s
Dividing both sides by 4, we get:
s = 12 cm
Now, we can find the area of the square using the formula:
Area = s^2
Substituting the value of 's', we have:
Area = 12^2
Calculating, we get:
Area = 144 cm^2
Therefore, the answer is A: 144 cm^2.

To find the perimeter of a regular pentagon with each side measuring 3 cm, we can use the formula:
Perimeter = Number of sides * Length of each side
Given that the length of each side is 3 cm, and a regular pentagon has 5 sides, we can substitute these values into the formula:
Perimeter = 5 * 3 cm
Now, we can calculate the perimeter:
Perimeter = 15 cm
Therefore, the perimeter of the regular pentagon is 15 cm.
Answer: D. 15 cm

To find the perimeter of an isosceles triangle, we need to add the lengths of all three sides.
Given:
- Two equal sides of 8 cm each
- Third side of 6 cm
We can calculate the perimeter as follows:
1. Add the lengths of all three sides:
- Two equal sides: 8 cm + 8 cm = 16 cm
- Third side: 6 cm
2. Add the lengths of all three sides:
- 16 cm + 6 cm = 22 cm
Therefore, the perimeter of the isosceles triangle is 22 cm.
Answer: B (22 cm)

Perimeter of a rectangle = length + breadth + length + breadth = 2(length + breadth)
To solve this problem, we can follow these steps:
1. Identify the formula for the perimeter of a rectangle: The perimeter of a rectangle is equal to twice the sum of its length and breadth.
2. Plug in the values given in the question: The question states that the perimeter of the rectangle is equal to _________ × (length + breadth).
3. Simplify the equation: Since the perimeter is equal to 2(length + breadth), we can rewrite the equation as 2(length + breadth) = _________ × (length + breadth).
4. Solve for the missing value: To find the missing value, divide both sides of the equation by (length + breadth). This will give us the value of _______, which is equal to 2.
5. Determine the correct answer: The question asks for the missing value, and we have found that the missing value is 2. Therefore, the correct answer is A.
In conclusion, the perimeter of a rectangle is equal to 2 times the sum of its length and breadth. The missing value in the given equation is 2, making the correct answer A.

To find the perimeter of any polygon, including a triangle, we need to add up the lengths of all its sides.
In the case of an equilateral triangle, all three sides have the same length. Let's call this length "s".
The perimeter of the equilateral triangle can be calculated by multiplying the length of one side by 3, as each side is equal in length.
Perimeter of an equilateral triangle = 3 × length of a side
Let's break down the solution into bullet points:
- An equilateral triangle is a triangle in which all three sides are equal in length.
- The formula for the perimeter of an equilateral triangle is the length of one side multiplied by 3.
- Therefore, the correct answer is A: equilateral triangle.
Remember, an equilateral triangle is a special case of a triangle where all sides are equal, so its perimeter can be calculated using a specific formula.

Problem:
A farmer has a rectangular field of length and breadth 240 m and 180 m respectively. He wants to fence it with 3 rounds of rope. What is the total length of rope he must use?

To calculate the total length of rope needed, we need to consider the perimeter of the rectangular field and the number of rounds of rope required.
Given:
- Length of the rectangular field: 240 m
- Breadth of the rectangular field: 180 m
- Number of rounds of rope: 3
Calculating the perimeter:
- Perimeter of a rectangle = 2 × (Length + Breadth)
Using the given values:
- Perimeter = 2 × (240 m + 180 m)
- Perimeter = 2 × 420 m
- Perimeter = 840 m
Calculating the total length of rope needed:
- Total length of rope = Perimeter × Number of rounds
Using the calculated perimeter and given number of rounds:
- Total length of rope = 840 m × 3
- Total length of rope = 2520 m
Therefore, the farmer must use a total length of 2520 m of rope to fence the rectangular field with 3 rounds.
Final Answer:
The correct answer is B. 2520 m.

To solve this problem, we need to understand the relationship between the area and perimeter of a rectangle.
1. Area of a rectangle:
The area of a rectangle is given by the formula:
Area = length × width
2. Perimeter of a rectangle:
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (length + width)
3. Relationship between area and perimeter:
If the area of a rectangle increases, it means that either the length or width or both have increased. Let's consider the possible scenarios:
- If only the length increases while the width remains the same, the perimeter will increase.
- If only the width increases while the length remains the same, the perimeter will increase.
- If both the length and width increase proportionally, the perimeter will increase.
- If both the length and width increase, but not proportionally, the perimeter will still increase.
4. Applying the concepts to the given problem:
In the given problem, the area of the rectangle increases from 2 cm^2 to 4 cm^2. This means that either the length or width or both have increased.
- If only the length increases while the width remains the same, the perimeter will increase.
- If only the width increases while the length remains the same, the perimeter will increase.
- If both the length and width increase proportionally, the perimeter will increase.
- If both the length and width increase, but not proportionally, the perimeter will still increase.
Therefore, we can conclude that the perimeter will increase when the area of the rectangle increases from 2 cm^2 to 4 cm^2.
Hence, the correct answer is B. increases.

To determine which figure encloses more area, we need to calculate the area of each figure and compare them.
1. Square:
- Side length = 2 cm
- Area = Side length * Side length = 2 cm * 2 cm = 4 cm²
2. Rectangle:
- Length = 3 cm
- Width = 2 cm
- Area = Length * Width = 3 cm * 2 cm = 6 cm²
3. Equilateral Triangle:
- Side length = 4 cm
- The formula to calculate the area of an equilateral triangle is given by:
Area = (√3 / 4) * Side length²
- Plugging in the values, we get:
Area = (√3 / 4) * 4 cm * 4 cm = (√3 / 4) * 16 cm² ≈ 6.93 cm²
Comparing the Areas:
From the calculations above, we can see that:
- The square has an area of 4 cm².
- The rectangle has an area of 6 cm².
- The equilateral triangle has an area of approximately 6.93 cm².
Therefore, the equilateral triangle encloses the largest area among the given figures.
Answer: C. equilateral triangle