Problem 336 - Prealgebra

Question

In the following exercises, solve. Gardening June has a vegetable garden in her yard. The garden is rectangular, with length 23 feet and width 28 feet. What is the area of the garden?

Step-by-Step Solution

Answer

The area of the garden is 644 square feet.

Step 1: Understand the Problem

The problem asks for the area of a rectangular garden. You need to find the area using the given length and width.

Step 2: Identify Given Values

The length of the garden is 23 feet and the width is 28 feet.

Step 3: Use the Area Formula

The formula for the area of a rectangle is \(\text{Area} = \text{length} \times \text{width}\).

Step 4: Substitute the Values

Substitute the given values into the formula: \(\text{Area} = 23 \text{ feet} \times 28 \text{ feet}\).

Step 5: Calculate the Area

Perform the multiplication: \(\text{Area} = 23 \times 28 = 644 \text{ square feet}\).

Step 6: State the Answer

The area of June's vegetable garden is 644 square feet.

Key Concepts

area calculation

To calculate the area of June's rectangular garden, you first need to understand what area represents. Area measures the surface space of a two-dimensional shape, such as a garden, a room, or even a piece of paper. In essence, area tells you how much space there is within the boundary of the shape. For a rectangle, like June's garden, the area can be found by multiplying its length by its width. You can use the formula: \[ \text{Area} = \text{length} \times \text{width} \]
The unit of area is always in square units, depending on the units used for length and width. In this case, since the length and width are measured in feet, the area will be in square feet.

rectangles

Rectangles are four-sided shapes (quadrilaterals) characterized by having opposite sides that are equal in length and four right angles. This makes them a specific type of parallelogram.
When dealing with real-world problems, like June's garden, you often encounter rectangular shapes because they are practical and easy to work with.
Understanding the properties of rectangles allows us to apply the area formula correctly. Since opposite sides are equal and the angles are all 90 degrees, calculating the area becomes straightforward with just the length and width. These properties make rectangles a common subject of study for basic geometry and area calculation problems.

multiplication

Multiplication is a fundamental arithmetic operation that allows you to find the total number of units in equal groups. In the context of area calculation, multiplication helps us determine the total space within a rectangle.
For June's garden, with a length of 23 feet and a width of 28 feet, the multiplication process involves calculating: \[ 23 \times 28 \]
To multiply these numbers, you can break it down step-by-step or use a calculator for quick results. The multiplication of 23 and 28 results in 644. Therefore, the area of the garden is \[ 644 \text{ square feet} \]
Remember, mastering multiplication not only helps in area calculation but also in a wide range of mathematical and real-life applications.