A Room 12 M By 10 M Has A Carpet Laid In The Centre Leaving 1 M Space All Around. What Is The Area Of The Carpet And The Uncovered Area?

Mar 10, 2025 by ADMIN 138 views

A Room with a Carpet: Calculating the Area of the Carpet and the Uncovered Space

When it comes to measuring the area of a room with a carpet, it's essential to consider the space left uncovered around the carpet. In this article, we will explore how to calculate the area of the carpet and the uncovered space in a room that is 12 meters by 10 meters, with a carpet laid in the center, leaving 1 meter of space all around.

To calculate the area of the carpet, we need to find the dimensions of the carpet. Since the carpet is laid in the center of the room, leaving 1 meter of space all around, we can subtract 2 meters from the length and width of the room to find the dimensions of the carpet.

The length of the room is 12 meters, and the width is 10 meters. To find the length of the carpet, we subtract 2 meters from the length of the room:

12 meters (length of the room) - 2 meters (space on each side) = 10 meters (length of the carpet)

Similarly, to find the width of the carpet, we subtract 2 meters from the width of the room:

10 meters (width of the room) - 2 meters (space on each side) = 8 meters (width of the carpet)

Now that we have the dimensions of the carpet, we can calculate its area by multiplying the length and width:

Area of the carpet = length x width = 10 meters x 8 meters = 80 square meters

To calculate the uncovered area, we need to find the area of the room that is not covered by the carpet. We can do this by finding the area of the room and subtracting the area of the carpet.

The area of the room is:

Area of the room = length x width = 12 meters x 10 meters = 120 square meters

Now, we subtract the area of the carpet from the area of the room to find the uncovered area:

Uncovered area = area of the room - area of the carpet = 120 square meters - 80 square meters = 40 square meters

In conclusion, to calculate the area of the carpet and the uncovered space in a room that is 12 meters by 10 meters, with a carpet laid in the center, leaving 1 meter of space all around, we need to find the dimensions of the carpet and the area of the room. By subtracting the space on each side from the length and width of the room, we can find the dimensions of the carpet, and by multiplying the length and width of the carpet, we can calculate its area. Finally, by subtracting the area of the carpet from the area of the room, we can find the uncovered area.

This problem can be applied to real-life scenarios, such as:

A homeowner wants to buy a carpet for their living room, but they need to know the area of the carpet to determine the cost.
A contractor needs to calculate the area of the carpet to determine the amount of material needed for a project.
A interior designer wants to create a design for a room with a carpet, but they need to know the area of the carpet to ensure that the design fits the space.

If the carpet is not laid in the center of the room, but rather in a corner, we would need to adjust the dimensions of the carpet accordingly.
If the room has a non-rectangular shape, we would need to use a different method to calculate the area of the carpet and the uncovered space.
If the carpet is not a perfect rectangle, we would need to use a different method to calculate the area of the carpet.

Area of the carpet = length x width
Uncovered area = area of the room - area of the carpet

[1] "Area of a Rectangle" by Math Open Reference
[2] "Calculating the Area of a Room" by The Spruce

Note: The references provided are for informational purposes only and are not directly related to the problem at hand.
A Room with a Carpet: Q&A

In our previous article, we explored how to calculate the area of the carpet and the uncovered space in a room that is 12 meters by 10 meters, with a carpet laid in the center, leaving 1 meter of space all around. In this article, we will answer some frequently asked questions related to this problem.

A: If the carpet is not laid in the center of the room, we would need to adjust the dimensions of the carpet accordingly. For example, if the carpet is laid in a corner, we would need to find the dimensions of the carpet by subtracting the space on each side from the length and width of the room, and then adjust the dimensions to fit the corner.

A: If the room has a non-rectangular shape, we would need to use a different method to calculate the area of the carpet and the uncovered space. For example, we could use the formula for the area of a polygon, which is:

Area = (n x s^2) / (4 x tan(π/n))

where n is the number of sides of the polygon, and s is the length of each side.

A: If the carpet is not a perfect rectangle, we would need to use a different method to calculate the area of the carpet. For example, we could use the formula for the area of a trapezoid, which is:

Area = (1/2) x (a + b) x h

where a and b are the lengths of the two parallel sides, and h is the height of the trapezoid.

A: Yes, you can use a calculator to calculate the area of the carpet. In fact, it's often easier to use a calculator than to do the calculations by hand. Just make sure to enter the correct values and follow the correct order of operations.

A: If you make a mistake in your calculations, don't worry! It's easy to make mistakes, especially when working with complex calculations. Just double-check your work, and if you're still unsure, try redoing the calculations from scratch.

A: No, this method is only suitable for rooms with a single level. If you have a room with multiple levels, you would need to use a different method to calculate the area of the carpet.

A: No, this method is only suitable for rooms with a flat ceiling. If you have a room with a sloping ceiling, you would need to use a different method to calculate the area of the carpet.

In conclusion, calculating the area of a carpet in a room can be a complex task, but with the right tools and techniques, it's easy to get the job done. We hope this Q&A article has been helpful in answering some of the most frequently asked questions related to this problem.

This problem can be applied to real-life scenarios, such as:

A homeowner wants to buy a carpet for their living room, but they need to know the area of the carpet to determine the cost.
A contractor needs to calculate the area of the carpet to determine the amount of material needed for a project.
A interior designer wants to create a design for a room with a carpet, but they need to know the area of the carpet to ensure that the design fits the space.

If you're working with a room with a non-rectangular shape, try using a different method to calculate the area of the carpet.
If you're working with a room with a sloping ceiling, try using a different method to calculate the area of the carpet.
If you're working with a room with multiple levels, try using a different method to calculate the area of the carpet.

Area of the carpet = length x width
Uncovered area = area of the room - area of the carpet

[1] "Area of a Rectangle" by Math Open Reference
[2] "Calculating the Area of a Room" by The Spruce

Note: The references provided are for informational purposes only and are not directly related to the problem at hand.