A room has a floor area of 48 square meters. What is the area of the room in square feet? Use the conversion: 1 meter = 3.28084 feet.
The correct answer and explanation is:
To convert the area of the room from square meters to square feet, you need to square the conversion factor for length. Since 1 meter equals 3.28084 feet, to find the area in square feet, you multiply the area in square meters by the square of the conversion factor.
The formula for converting square meters to square feet is: Area in square feet=Area in square meters×(3.28084)2\text{Area in square feet} = \text{Area in square meters} \times (3.28084)^2
Now, let’s perform the conversion: Area in square feet=48 m2×(3.28084)2\text{Area in square feet} = 48 \, \text{m}^2 \times (3.28084)^2 Area in square feet=48 m2×10.7639\text{Area in square feet} = 48 \, \text{m}^2 \times 10.7639 Area in square feet=516.67 ft2\text{Area in square feet} = 516.67 \, \text{ft}^2
So, the area of the room is 516.67 square feet.
Explanation
The conversion involves two steps. First, you use the conversion factor for meters to feet, which is 1 meter = 3.28084 feet. When converting area, the conversion factor for length needs to be squared because you are dealing with two dimensions (length and width). So, you square the length conversion factor to get the appropriate conversion for area.
The result gives the area in square feet, which in this case is 516.67 square feet. This is a useful method for changing between metric and imperial systems, especially in areas like real estate or construction where area measurements are often required in square feet or square meters depending on the region.
By using this method, you can easily convert between different units of measurement when needed, ensuring that calculations are accurate.