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Chapter 1: Problem 27

Find the area of a rectangle with length 15 meters and width \(2.3\) meters.

Short Answer

Expert verified
The area of the rectangle is 34.5 square meters.

Step by step solution

01

Identify the formula for the area of a rectangle

The area of a rectangle is calculated by multiplying its length by its width. The formula is: \[ \text{Area} = \text{Length} \times \text{Width} \]
02

Insert the given values into the formula

We know the length of the rectangle is 15 meters, and the width is 2.3 meters. Insert these values into the formula: \[ \text{Area} = 15 \times 2.3 \]
03

Perform the calculation

Now, we need to multiply 15 by 2.3. Perform this calculation: \[ 15 \times 2.3 = 34.5 \] So, the area of the rectangle is 34.5 square meters.

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Key Concepts

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

Geometric Formulas
Understanding geometric formulas is key to solving problems involving shapes like rectangles. A formula is simply a way of expressing a relationship between different measurements.
In the case of a rectangle, the most important formula relates its length and width to its area.
The area of a rectangle is the total space that the rectangle covers in a flat plane.
  • The formula for finding this area is: \[ \text{Area} = \text{Length} \times \text{Width} \] This tells us that the area is calculated by multiplying the length of the rectangle by its width.
Using formulas helps not only in mathematics but also in real-life situations, like calculating materials needed for construction or carpet area for rooms.
Multiplication
Multiplication is one of the fundamental arithmetic operations, much like addition, subtraction, and division, and it plays a major role in calculating the area of a rectangle. When you multiply two numbers, you are essentially adding one number to itself multiple times.
For example, when calculating the area,
  • if you multiply the length (15 meters) by the width (2.3 meters),
    you are determining how many square meters are covered by the rectangle.
In the problem given, you use multiplication to find that \[ 15 \times 2.3 = 34.5 \]This tells us there are 34.5 square meters in total inside the boundaries of the rectangle. Multiplication makes it straightforward to calculate areas quickly and efficiently.
Measurement Units
Measurement units help us understand and communicate the size, amount, or degree of something. They are essential in ensuring that we can compare and compute measurements accurately.
In geometry, when calculating area, the units denote how large or small a space is.
  • For a rectangle, if the measurements for length and width are in meters, the area is expressed in square meters (\(\text{m}^2\)).
This means that for every meter of width and length, you cover a square meter of area.
In the example calculation, the area of 34.5 square meters indicates that if plotted on a field, the rectangle would cover that much space. Understanding units is important as they help provide context and meaning to the numbers we compute.

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