Taylor Wants To Paint His Rectangular Deck That Is 42 Feet Long And 28 Feet Wide. A Gallon Of Paint Covers About 350 Square Feet. How Many Gallons Of Paint Will Taylor Need To Cover The Entire Deck?Write And Solve An Equation To Find The Area Of The Deck.

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Understanding the Problem

Taylor wants to paint his rectangular deck, which is 42 feet long and 28 feet wide. To determine how many gallons of paint he will need, we first need to calculate the area of the deck. The area of a rectangle is calculated by multiplying its length by its width.

Calculating the Area of the Deck

To find the area of the deck, we can use the formula:

Area = Length x Width

In this case, the length of the deck is 42 feet, and the width is 28 feet. Plugging these values into the formula, we get:

Area = 42 x 28

Solving the Equation

To solve the equation, we multiply 42 by 28:

42 x 28 = 1176

Therefore, the area of the deck is 1176 square feet.

Determining the Number of Gallons of Paint Needed

Now that we know the area of the deck, we can determine how many gallons of paint Taylor will need. A gallon of paint covers about 350 square feet. To find out how many gallons of paint are needed, we can divide the area of the deck by the coverage of a gallon of paint:

Gallons of Paint = Area of Deck / Coverage per Gallon

Plugging in the values, we get:

Gallons of Paint = 1176 / 350

Solving the Equation

To solve the equation, we divide 1176 by 350:

1176 ÷ 350 = 3.34

Therefore, Taylor will need approximately 3.34 gallons of paint to cover the entire deck.

Rounding Up to the Nearest Whole Number

Since we can't buy a fraction of a gallon of paint, we need to round up to the nearest whole number. In this case, we round up to 4 gallons of paint.

Conclusion

In conclusion, to calculate the area of a rectangular deck, we multiply its length by its width. To determine how many gallons of paint are needed, we divide the area of the deck by the coverage of a gallon of paint. In this case, Taylor will need approximately 4 gallons of paint to cover the entire deck.

Additional Tips and Considerations

  • Make sure to read the label on the paint can to ensure that it covers the desired area.
  • Consider the surface texture and porosity of the deck when calculating the number of gallons of paint needed.
  • If the deck has any obstacles or irregularities, you may need to add extra paint to cover these areas.

Real-World Applications

Calculating the area of a rectangular deck is a common problem in real-world applications, such as:

  • Painting a deck or patio
  • Calculating the cost of materials for a construction project
  • Determining the size of a room or space

Mathematical Concepts

This problem involves the following mathematical concepts:

  • Multiplication
  • Division
  • Fractions
  • Rounding numbers

Practice Problems

Try solving the following practice problems:

  • A rectangular room has a length of 25 feet and a width of 15 feet. What is the area of the room?
  • A gallon of paint covers about 400 square feet. How many gallons of paint are needed to cover a deck that is 50 feet long and 30 feet wide?
    Frequently Asked Questions (FAQs) About Calculating the Area of a Rectangular Deck =====================================================================================

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

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

Area = Length x Width

Q: How do I calculate the area of a deck with irregular shapes or obstacles?

A: To calculate the area of a deck with irregular shapes or obstacles, you can break down the deck into smaller, more manageable sections. Calculate the area of each section separately and then add them together to get the total area.

Q: What if I have a deck with a complex shape, such as a L-shape or a U-shape?

A: To calculate the area of a deck with a complex shape, you can use the following steps:

  1. Break down the deck into smaller, more manageable sections.
  2. Calculate the area of each section separately.
  3. Add the areas of each section together to get the total area.

Q: How do I account for the surface texture and porosity of the deck when calculating the number of gallons of paint needed?

A: To account for the surface texture and porosity of the deck, you can use the following steps:

  1. Research the surface texture and porosity of the deck material.
  2. Adjust the coverage rate of the paint accordingly.
  3. Recalculate the number of gallons of paint needed based on the adjusted coverage rate.

Q: What if I'm not sure about the length or width of the deck?

A: If you're not sure about the length or width of the deck, you can use the following steps:

  1. Measure the length and width of the deck using a tape measure.
  2. Record the measurements accurately.
  3. Use the measurements to calculate the area of the deck.

Q: Can I use a calculator to calculate the area of a deck?

A: Yes, you can use a calculator to calculate the area of a deck. Simply enter the length and width of the deck into the calculator and multiply them together to get the area.

Q: What if I make a mistake when calculating the area of the deck?

A: If you make a mistake when calculating the area of the deck, you can use the following steps:

  1. Review your calculations carefully.
  2. Check your measurements and calculations for accuracy.
  3. Recalculate the area of the deck using the correct measurements and calculations.

Q: Can I use a formula to calculate the number of gallons of paint needed?

A: Yes, you can use a formula to calculate the number of gallons of paint needed. The formula is:

Gallons of Paint = Area of Deck / Coverage per Gallon

Q: What if I'm not sure about the coverage rate of the paint?

A: If you're not sure about the coverage rate of the paint, you can use the following steps:

  1. Research the coverage rate of the paint.
  2. Check the label on the paint can for the coverage rate.
  3. Use the coverage rate to calculate the number of gallons of paint needed.

Q: Can I use a calculator to calculate the number of gallons of paint needed?

A: Yes, you can use a calculator to calculate the number of gallons of paint needed. Simply enter the area of the deck and the coverage rate of the paint into the calculator and divide them to get the number of gallons of paint needed.