Sammy Has A Rectangular Doormat On Her Porch. The Mat Is $\frac{4}{5}$ M Long And $\frac{1}{2}$ M Wide.What Is The Area Of The Doormat?$\square \ M^2$

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Introduction

When it comes to measuring the area of a rectangular doormat, it's essential to understand the concept of area and how to calculate it. The area of a rectangle is determined by multiplying its length by its width. In this article, we will explore how to calculate the area of a rectangular doormat using the given dimensions.

Understanding the Dimensions

The rectangular doormat on Sammy's porch has a length of 45\frac{4}{5} m and a width of 12\frac{1}{2} m. To calculate the area, we need to multiply these two dimensions together.

Calculating the Area

To calculate the area of the doormat, we multiply the length by the width:

Area=Length×Width\text{Area} = \text{Length} \times \text{Width}

Area=45×12\text{Area} = \frac{4}{5} \times \frac{1}{2}

To multiply fractions, we multiply the numerators together and the denominators together:

Area=4×15×2\text{Area} = \frac{4 \times 1}{5 \times 2}

Area=410\text{Area} = \frac{4}{10}

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

Area=4÷210÷2\text{Area} = \frac{4 \div 2}{10 \div 2}

Area=25\text{Area} = \frac{2}{5}

Converting the Fraction to a Decimal

To make the area easier to understand, we can convert the fraction to a decimal:

Area=25=0.4\text{Area} = \frac{2}{5} = 0.4

Conclusion

In conclusion, the area of the rectangular doormat on Sammy's porch is 25\frac{2}{5} m2^2, which is equivalent to 0.4 m2^2. This calculation demonstrates the importance of understanding the concept of area and how to calculate it using the given dimensions.

Real-World Applications

Calculating the area of a rectangular doormat may seem like a simple task, but it has real-world applications in various fields, such as:

  • Interior Design: When designing a room, it's essential to calculate the area of the floor to determine the amount of flooring material needed.
  • Construction: Builders need to calculate the area of rooms, walls, and floors to ensure that the materials are sufficient for the project.
  • Landscaping: When designing a garden or a landscape, it's crucial to calculate the area of the space to determine the amount of plants, soil, and other materials needed.

Tips and Tricks

Here are some tips and tricks to help you calculate the area of a rectangular doormat:

  • Use a calculator: When working with fractions, it's often easier to use a calculator to simplify the calculation.
  • Simplify the fraction: Before multiplying the fractions, simplify them by dividing both the numerator and the denominator by their greatest common divisor.
  • Convert to a decimal: To make the area easier to understand, convert the fraction to a decimal.

Common Mistakes

Here are some common mistakes to avoid when calculating the area of a rectangular doormat:

  • Forgetting to multiply: Make sure to multiply the length by the width to get the correct area.
  • Not simplifying the fraction: Simplify the fraction before multiplying to avoid unnecessary calculations.
  • Not converting to a decimal: Convert the fraction to a decimal to make the area easier to understand.

Conclusion

Q: What is the formula for calculating the area of a rectangular doormat?

A: The formula for calculating the area of a rectangular doormat is:

Area=Length×Width\text{Area} = \text{Length} \times \text{Width}

Q: How do I calculate the area of a rectangular doormat with mixed numbers?

A: To calculate the area of a rectangular doormat with mixed numbers, you need to convert the mixed numbers to improper fractions. For example, if the length is 2 12\frac{1}{2} m and the width is 3 14\frac{1}{4} m, you would convert them to improper fractions as follows:

Length=212=52\text{Length} = 2 \frac{1}{2} = \frac{5}{2}

Width=314=134\text{Width} = 3 \frac{1}{4} = \frac{13}{4}

Then, you would multiply the length by the width:

Area=52×134\text{Area} = \frac{5}{2} \times \frac{13}{4}

Q: How do I calculate the area of a rectangular doormat with decimals?

A: To calculate the area of a rectangular doormat with decimals, you can multiply the length by the width as follows:

Area=Length×Width\text{Area} = \text{Length} \times \text{Width}

For example, if the length is 2.5 m and the width is 3.25 m, you would multiply them together:

Area=2.5×3.25=8.125\text{Area} = 2.5 \times 3.25 = 8.125

Q: What is the difference between the area of a rectangular doormat and the perimeter?

A: The area of a rectangular doormat is the amount of space inside the mat, while the perimeter is the distance around the mat. To calculate the perimeter, you need to add up the lengths of all four sides of the mat.

Q: How do I calculate the perimeter of a rectangular doormat?

A: To calculate the perimeter of a rectangular doormat, you need to add up the lengths of all four sides of the mat. The formula for the perimeter is:

Perimeter=2×(Length+Width)\text{Perimeter} = 2 \times (\text{Length} + \text{Width})

For example, if the length is 2 m and the width is 3 m, you would calculate the perimeter as follows:

Perimeter=2×(2+3)\text{Perimeter} = 2 \times (2 + 3)

Perimeter=2×5\text{Perimeter} = 2 \times 5

Perimeter=10\text{Perimeter} = 10

Q: What is the relationship between the area and the perimeter of a rectangular doormat?

A: The area and the perimeter of a rectangular doormat are related in that the perimeter is the distance around the mat, while the area is the amount of space inside the mat. However, the area and the perimeter are not directly proportional. The area is proportional to the length and width of the mat, while the perimeter is proportional to the sum of the length and width.

Q: How do I use the area and perimeter of a rectangular doormat in real-world applications?

A: The area and perimeter of a rectangular doormat can be used in various real-world applications, such as:

  • Interior Design: When designing a room, you need to calculate the area of the floor to determine the amount of flooring material needed. You also need to calculate the perimeter of the room to determine the amount of baseboard and molding needed.
  • Construction: Builders need to calculate the area of rooms, walls, and floors to ensure that the materials are sufficient for the project. They also need to calculate the perimeter of the building to determine the amount of siding and trim needed.
  • Landscaping: When designing a garden or a landscape, you need to calculate the area of the space to determine the amount of plants, soil, and other materials needed. You also need to calculate the perimeter of the space to determine the amount of edging and mulch needed.

Q: What are some common mistakes to avoid when calculating the area and perimeter of a rectangular doormat?

A: Some common mistakes to avoid when calculating the area and perimeter of a rectangular doormat include:

  • Forgetting to multiply: Make sure to multiply the length by the width to get the correct area.
  • Not simplifying the fraction: Simplify the fraction before multiplying to avoid unnecessary calculations.
  • Not converting to a decimal: Convert the fraction to a decimal to make the area easier to understand.
  • Not adding up the sides: Make sure to add up the lengths of all four sides of the mat to get the correct perimeter.

By following these tips and avoiding common mistakes, you can ensure that you get the correct area and perimeter of a rectangular doormat.