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Chapter 2: Problem 163

Find the area of a rectangle that measures 4.5 in. by 3.25 in. Use the formula \(A=L W\)

Short Answer

Expert verified
The area of the rectangle is 14.625 square inches.

Step by step solution

01

Identify given values

Identify the given values. In this case, length(L) = 4.5 inches and width(W) = 3.25 inches.
02

Apply the formula

Apply the formula for the area of a rectangle which is \(A=L W\). Substitute the given values into the formula.
03

Calculate

Do the calculation. Multiply the length and width to find the area. \(A=4.5 in. \times 3.25 in.\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calculating Area
To find the area of a rectangle, we need to determine how much surface the shape covers. The area tells us how many square units fit inside the rectangle. We use the formula for the area of a rectangle:
  • The formula is:
    \(A = L \times W\)
In this formula:
- \(A\) represents the area.
- \(L\) represents the length of the rectangle.
- \(W\) represents the width of the rectangle.
Simply multiply the length by the width to calculate the area. When dealing with real-life examples, make sure the units are consistent, such as inches or centimeters.
Rectangle Dimensions
Understanding the dimensions of a rectangle is crucial for calculating its area. Dimensions refer to the measurements that describe a rectangle's size:
  • **Length (L):** This is the longer side of the rectangle in most cases.
    In this problem, the length is given as 4.5 inches.
  • **Width (W):** This is the shorter side of the rectangle.
    In this problem, the width is given as 3.25 inches.
Having these measurements allows us to apply them to the area formula. Even if the length and width are the same (as in a square), the calculation method remains the same. If given different units, you should convert them to the same unit for accuracy.
Multiplication in Geometry
Multiplication is at the core of finding the area of a rectangle in geometry. Unlike addition, which gives us totals, multiplication helps us determine how one value repeatedly adds up. Here鈥檚 how multiplication applies in this context:
  • **Geometric Interpretation:** Imagine a grid laid over the rectangle, where each square represents one square inch.
    Multiplying length by width counts how many of these squares fill the rectangle.
  • **Example Calculation:** For our rectangle with length 4.5 inches and width 3.25 inches, you multiply: \(4.5 \times 3.25\).
    This results in 14.625 square inches.
This illustrates how multiplication in geometry allows us to quickly calculate large areas, much faster than adding each square individually.

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Most popular questions from this chapter

Use newspapers or the Internet to find and list situations in which decimals are used. Determine whether the decimals you find are exact values or approximations. INote: Large numbers (such as 3.2 billion) used to describe values such as the balance of trade or the national debt are approximations. Smaller numbers (such as 1.5866 ) used to describe business transactions such as an exchange rate or a stock price are exact values.]

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{8}{15} \quad 0.543$$

Use the formula \(M=S-C,\) where \(M\) is the markup on a consumer product, \(S\) is the selling price, and \(C\) is the cost of the product to the business, to find the markup on a product that cost a business \(\$ 1653.19\) and has a selling price of \(\$ 2231.81\)

What is the largest fraction with a denominator of 5 that is less than \(0.78 ?\)

Divide and round to the nearest hundredth. Then check by estimating the quotient. $$6.398 \div 5.5$$
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