15 feet by 120 inches area
The Correct Answer and Explanation is :
To calculate the area of a rectangle, you multiply its length by its width. In this case, you have dimensions given in two different units: feet and inches. To find the area in a consistent unit, we need to convert one of the measurements.
First, let’s convert the 15 feet into inches. Since there are 12 inches in a foot:
[
15 \text{ feet} \times 12 \text{ inches/foot} = 180 \text{ inches}
]
Now, you have the dimensions of the rectangle as 180 inches by 120 inches. Now, we can calculate the area:
[
\text{Area} = \text{Length} \times \text{Width} = 180 \text{ inches} \times 120 \text{ inches}
]
[
\text{Area} = 21600 \text{ square inches}
]
Thus, the area of the rectangle is 21,600 square inches.
Explanation
Calculating the area of a rectangle is a fundamental concept in geometry. The area represents the amount of space enclosed within the rectangle’s boundaries. It is usually expressed in square units, which in this case are square inches.
The dimensions of a rectangle are typically provided in the same unit of measurement. In this scenario, we initially have one measurement in feet (15 feet) and another in inches (120 inches). To ensure consistency, converting the feet measurement into inches simplifies calculations and avoids confusion.
The conversion factor between feet and inches (12 inches per foot) allows us to make this transition easily. Once both measurements are in inches, we can multiply them directly.
The multiplication process yields the area in square inches, a unit suitable for smaller measurements or detailed designs. Understanding how to convert units and calculate area is crucial not only in mathematics but also in fields such as architecture, engineering, and even landscaping, where precise area measurements are essential for planning and material estimation.
In summary, the area of the rectangle defined by the dimensions of 15 feet and 120 inches is 21,600 square inches, which exemplifies how unit conversion and basic multiplication can effectively determine the space within a defined shape.