The Floor Of A Building Consists Of 2500 Tiles Which Are Rhombus Shaped And Its Diagonals Are 30 And 15 In Length. Find The Total Cost Of Polishing The Floor, If The Cost Of Polishing Per M² Is Rs 10.​

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Introduction

When it comes to calculating the cost of polishing a floor, several factors come into play. The total area of the floor, the cost of polishing per square meter, and the number of tiles are just a few of the key considerations. In this article, we will delve into a real-world scenario where a building's floor consists of 2500 rhombus-shaped tiles, each with diagonals measuring 30 and 15 inches in length. Our goal is to determine the total cost of polishing the floor, given that the cost of polishing per square meter is Rs 10.

Understanding Rhombus-Shaped Tiles

A rhombus is a type of quadrilateral with all sides of equal length. Its diagonals bisect each other at right angles, creating four right-angled triangles. In this case, the diagonals of each tile measure 30 and 15 inches. To calculate the area of each tile, we need to find the length of the sides of the rhombus.

Calculating the Area of Each Tile

To find the area of each tile, we can use the formula for the area of a rhombus:

Area = (d1 × d2) / 2

where d1 and d2 are the lengths of the diagonals.

Plugging in the values, we get:

Area = (30 × 15) / 2 = 450 / 2 = 225 square inches

Converting the Area to Square Meters

To convert the area from square inches to square meters, we need to perform two conversions: inches to meters and square inches to square meters.

1 inch = 0.0254 meters 1 square inch = 0.00064516 square meters

Using these conversion factors, we can convert the area of each tile from square inches to square meters:

Area (square meters) = 225 × 0.00064516 = 0.1451 square meters

Calculating the Total Area of the Floor

Now that we have the area of each tile in square meters, we can calculate the total area of the floor by multiplying the area of each tile by the total number of tiles:

Total Area = Area (square meters) × Number of Tiles = 0.1451 × 2500 = 363.25 square meters

Calculating the Total Cost of Polishing the Floor

Given that the cost of polishing per square meter is Rs 10, we can calculate the total cost of polishing the floor by multiplying the total area by the cost per square meter:

Total Cost = Total Area × Cost per Square Meter = 363.25 × 10 = Rs 3632.50

Conclusion

In this article, we explored a real-world scenario where a building's floor consists of 2500 rhombus-shaped tiles, each with diagonals measuring 30 and 15 inches in length. By calculating the area of each tile and converting it to square meters, we determined the total area of the floor to be 363.25 square meters. Finally, we calculated the total cost of polishing the floor, given that the cost of polishing per square meter is Rs 10. The total cost of polishing the floor is Rs 3632.50.

Discussion

  • What are some other factors that can affect the cost of polishing a floor?
  • How can the area of each tile be calculated if the diagonals are not given?
  • What are some real-world applications of rhombus-shaped tiles?

References

Introduction

In our previous article, we explored a real-world scenario where a building's floor consists of 2500 rhombus-shaped tiles, each with diagonals measuring 30 and 15 inches in length. We calculated the total area of the floor to be 363.25 square meters and determined the total cost of polishing the floor to be Rs 3632.50. In this article, we will answer some frequently asked questions related to rhombus-shaped tiles and polishing costs.

Q&A

Q: What are some other factors that can affect the cost of polishing a floor?

A: Several factors can affect the cost of polishing a floor, including the type of flooring material, the size of the floor, the number of coats of polish required, and the labor costs. Additionally, the cost of polishing can also be affected by the location, with urban areas typically having higher costs than rural areas.

Q: How can the area of each tile be calculated if the diagonals are not given?

A: If the diagonals of a rhombus are not given, the area can be calculated using the formula:

Area = (a × b) / 2

where a and b are the lengths of the sides of the rhombus.

However, if only the diagonals are given, the area can be calculated using the formula:

Area = (d1 × d2) / 2

where d1 and d2 are the lengths of the diagonals.

Q: What are some real-world applications of rhombus-shaped tiles?

A: Rhombus-shaped tiles have several real-world applications, including:

  • Flooring: Rhombus-shaped tiles are often used in flooring due to their unique shape and ability to create a visually appealing pattern.
  • Architecture: Rhombus-shaped tiles can be used in architectural designs to create unique and interesting patterns.
  • Art: Rhombus-shaped tiles can be used in art projects to create unique and visually appealing designs.

Q: How can the cost of polishing a floor be reduced?

A: The cost of polishing a floor can be reduced by:

  • Using a lower-cost polishing material
  • Applying fewer coats of polish
  • Reducing the size of the floor
  • Using a more efficient polishing process

Q: What are some common mistakes to avoid when calculating the cost of polishing a floor?

A: Some common mistakes to avoid when calculating the cost of polishing a floor include:

  • Failing to account for the size of the floor
  • Failing to account for the number of coats of polish required
  • Failing to account for labor costs
  • Failing to account for location-specific costs

Q: How can the total area of a floor be calculated if the tiles are not all the same size?

A: If the tiles are not all the same size, the total area of the floor can be calculated by:

  • Measuring the length and width of each tile
  • Calculating the area of each tile
  • Adding up the areas of all the tiles

Alternatively, the total area of the floor can be calculated by:

  • Measuring the length and width of the floor
  • Calculating the area of the floor
  • Subtracting the areas of any gaps or irregularities

Conclusion

In this article, we answered some frequently asked questions related to rhombus-shaped tiles and polishing costs. We hope that this information has been helpful in understanding the complexities of calculating the cost of polishing a floor.

Discussion

  • What are some other factors that can affect the cost of polishing a floor?
  • How can the area of each tile be calculated if the diagonals are not given?
  • What are some real-world applications of rhombus-shaped tiles?

References