Problem 99 - Elementary Algebra

Question

Problem: The length of a rectangle is \(3 \mathrm{~cm}\). Its width is \(8 \mathrm{~cm}\). Find its area. $$ \text { Incorrect Answer: } \begin{aligned} A &=L W \\ A &=3 \cdot 8 \\ A &=24 \end{aligned} $$

Step-by-Step Solution

Answer

The area of the rectangle is 24 cm\textsuperscript{2}.

Step 1: Identify the Formula

The formula for the area of a rectangle is given by the product of its length (L) and width (W).

Step 2: Substitute the Values

Substitute the given values into the formula. Here, the length (L) is 3 cm, and the width (W) is 8 cm.

Step 3: Perform the Multiplication

Multiply the length by the width: \[ A = 3 \text{ cm} \times 8 \text{ cm} = 24 \text{ cm}^2 \]

Step 4: Interpret the Result

The calculated area of the rectangle is 24 square centimeters.

Key Concepts

Rectangle

A rectangle is a four-sided figure with opposite sides that are equal in length. Two opposite sides are called the length, and the other two sides are called the width. Rectangles are a fundamental shape in geometry, and you encounter them frequently in everyday objects like books, screens, and tables. Understanding rectangles is crucial because they form the basis for more complex geometric concepts.

Area Calculation

The area of a rectangle is a measure of how much space the rectangle covers. To calculate the area, you use the formula: \( A = L \times W \), where \(A\) represents the area, \(L\) is the length, and \(W\) is the width. This formula works because a rectangle can be visualized as being filled with smaller squares. For example, if the length is 3 cm and the width is 8 cm, you can fit three rows of eight small squares inside the rectangle, resulting in a total of 24 squares. Therefore, the area is 24 square centimeters.

Basic Geometry

Basic geometry involves understanding shapes, their properties, and how to measure them. For rectangles, it's important to note:

• Rectangles have four right angles (each 90 degrees).
• Opposite sides are not only equal but also parallel.

The concepts of length and width are crucial because they define the rectangle's dimensions. Being knowledgeable in basic geometry helps you easily solve problems related to shapes, size, and area. When you grasp these fundamental concepts, you can apply them to more advanced geometrical figures and calculations.