Question

Find the area \(A\) of a rectangle with length 6 inches and width 7 inches.

Short answer

The area \( A \) of the rectangle is 42 square inches.

Step-by-step solution

Understand the formula for the area of a rectangle

The area of a rectangle can be found using the formula \( A = \text{length} \times \text{width} \).

Insert the values for length and width

In this exercise, the length of the rectangle is given as 6 inches, and the width is given as 7 inches.

Calculate the area

Using the formula \( A = \text{length} \times \text{width} \), substitute the given values: \( A = 6 \text{ inches} \times 7 \text{ inches} \).

Simplify the multiplication

Perform the multiplication: \( 6 \times 7 = 42 \). Thus, the area \( A = 42 \text{ square inches} \).

Key concepts

area calculation

Calculating the area of a rectangle is a fundamental concept in geometry. The area signifies the amount of space enclosed within the rectangle. The formula used for calculating the area is straightforward:

\(A = \text{length} \times \text{width}\).
This formula multiplies the length of the rectangle (the longer side) by the width (the shorter side).
The resulting product gives the area, expressed in square units.
Understanding and applying this formula is essential for solving many geometric problems and real-world applications.
For example, in our given exercise, the length is 6 inches and the width is 7 inches, so we plug these numbers into our formula and calculate as follows:

\(A = 6 \text{ inches} \times 7 \text{ inches} = 42 \text{ square inches} \). This step-by-step method ensures accuracy and builds a strong foundation for more complex area calculations.

rectangle properties

A rectangle is a four-sided polygon, also known as a quadrilateral. The key properties of a rectangle which make it unique include:

• It has four right angles (90 degrees each), ensuring that opposite sides are parallel and of equal length.
• Its opposite sides are both equal and parallel.
• The diagonals of a rectangle are equal in length and bisect each other.

Knowing these properties helps in identifying a rectangle and understanding its geometric behavior. Rectangles are found in everyday objects, like screens, windows, and books, emphasizing the importance of comprehending their properties.

basic arithmetic

Basic arithmetic involves simple mathematical operations, such as addition, subtraction, multiplication, and division. These operations are essential for solving everyday problems and understanding more complex mathematical concepts.

Multiplication, as used in our area calculation of a rectangle, is a fundamental arithmetic operation. When multiplying two values, we're essentially adding one value (width in this case) repeatedly, as many times as the other value (length here) specifies.

For instance, in our exercise:
6 inches (length) repeated 7 times (width) gives us: 6+6+6+6+6+6+6 = 42 square inches.

This basic arithmetic principle underpins the area formula and helps reinforce why multiplication is a quicker method than repeated addition.