The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
Correct Answer: 6.72 m²
Explanation
To find the area of Leah’s office, we must first ensure both area measurements are in the same unit. The problem provides Kyrie’s office area in square meters (m²) and the additional area for Leah’s office in square centimeters (cm²). Since the final answer needs to be in square meters, the most direct approach is to convert the 4200 cm² into m².
The key to this conversion is understanding the relationship between meters and centimeters. We know that 1 meter is equal to 100 centimeters. However, when dealing with area, we are working with two dimensions, so we must square this relationship. A square meter (1 m²) represents an area that is 1 meter long by 1 meter wide. In centimeters, this would be 100 cm long by 100 cm wide.
Therefore, the conversion factor for area is:
1 m² = 100 cm × 100 cm = 10,000 cm²
Now we can convert the 4200 cm² into square meters by dividing it by 10,000.
4200 cm² ÷ 10,000 cm²/m² = 0.42 m²
This means that Leah’s office is 0.42 m² larger than Kyrie’s office.
With both values now in square meters, we can perform the final calculation. We add the size difference to the area of Kyrie’s office to find the total area of Leah’s office.
Area of Kyrie’s office = 6.3 m²
Additional area for Leah’s office = 0.42 m²
Total area of Leah’s office = 6.3 m² + 0.42 m² = 6.72 m²
Thus, the area of Leah’s office is 6.72 m². The process required converting the units to be consistent before performing the addition.
