All questions of Perimeter and Area for Class 6 Exam

To find the area of the remaining part of the land, we need to subtract the total area of the flower beds from the total area of the land.

1. Calculate the area of one flower bed:
- The flower bed is in the shape of a square.
- The side of the flower bed is given as 3cm.
- The area of a square is calculated by squaring the length of one side.
- Area of one flower bed = (3cm)² = 9cm²

2. Calculate the total area of all five flower beds:
- Since there are five flower beds, multiply the area of one flower bed by 5.
- Total area of flower beds = 5 * 9cm² = 45cm²

3. Convert the dimensions of the land from meters to centimeters:
- Length of the land = 17m = 1700cm
- Width of the land = 5m = 500cm

4. Calculate the total area of the land:
- Total area of the land = Length * Width
- Total area of the land = 1700cm * 500cm = 850,000cm²

5. Calculate the area of the remaining part of the land:
- Remaining area of the land = Total area of the land - Total area of flower beds
- Remaining area of the land = 850,000cm² - 45cm² = 849,955cm²

Therefore, the area of the remaining part of the land is 849,955cm². However, since the answer choices are given in square centimeters, we round the answer to the nearest whole number.
So, the correct answer is option B) 40cm².

Understanding the Problem
To find the perimeter of a rectangle when given its area and length, we can follow these steps:
Given Information
- Area of the rectangle = 630 cm²
- Length of the rectangle = 35 cm
Finding the Width
- The formula for the area of a rectangle is:
Area = Length × Width
- Rearranging the formula to find the width:
Width = Area ÷ Length
- Substitute the known values:
Width = 630 cm² ÷ 35 cm
- Performing the calculation:
Width = 18 cm
Calculating the Perimeter
- The formula for the perimeter of a rectangle is:
Perimeter = 2 × (Length + Width)
- Plugging in the values:
Perimeter = 2 × (35 cm + 18 cm)
- Adding the length and width:
Perimeter = 2 × 53 cm
- Performing the multiplication:
Perimeter = 106 cm
Conclusion
The perimeter of the rectangle is 106 cm, which corresponds to option 'C'. This method illustrates how to derive one measurement from another in basic geometry.
Thus, the correct choice is:
- Option C: 106 cm

Solution:
Given, the area of a square is 2401 cm^2.

To find the perimeter of the square, we need to know the length of its sides.

Let's assume the length of each side of the square is 'a' cm.

Finding the length of sides:
We know that the area of a square is given by the formula: area = side^2.
So, we can write the equation as:
2401 = a^2

Taking the square root on both sides of the equation, we get:
√2401 = √(a^2)

Simplifying, we get:
49 = a

So, the length of each side of the square is 49 cm.

Finding the perimeter of the square:
The perimeter of a square is given by the formula: perimeter = 4 * side.

Substituting the value of 'a' as 49 cm, we can calculate the perimeter as:
perimeter = 4 * 49
perimeter = 196 cm

Therefore, the perimeter of the square is 196 cm.

Hence, the correct answer is option C) 196 cm.

To find the perimeter of a regular hexagon, we need to know the length of one side. In this case, the length of each side is given as 6.5 cm.

Perimeter of a Hexagon:
A regular hexagon has six equal sides. The perimeter of a regular hexagon is calculated by multiplying the length of one side by 6.

Perimeter = Length of one side × 6

Given that the length of one side is 6.5 cm, we can substitute this value into the formula to find the perimeter.

Perimeter = 6.5 cm × 6

Calculating the Perimeter:
To calculate the perimeter, we can multiply 6.5 cm by 6.

Perimeter = 6.5 cm × 6
Perimeter = 39 cm

Therefore, the perimeter of the regular hexagon with each side measuring 6.5 cm is 39 cm.

To find the width of the room, we can use the formula for the area of a rectangle:

Area = Length × Width

Given that the length of the room is 8m and the cost of flooring is Rs 85/m2, we can calculate the total cost of flooring the room:

Total cost = Cost per square meter × Area

Given that the total cost is Rs 5100, we can substitute the values into the equation:

Rs 5100 = Rs 85/m2 × Area

Now, let's solve for the area:

Area = Rs 5100 / Rs 85/m2
Area = 60 m2

To find the width of the room, we can rearrange the formula for the area of a rectangle:

Width = Area / Length

Substituting the values into the equation:

Width = 60 m2 / 8 m
Width = 7.5 m

Therefore, the width of the room is 7.5 meters.

The correct answer is option B) 7.5 m.