Converting Units of Area
Convert units of area in Grade 9 math by squaring linear conversion factors—since area is two-dimensional, 1 ft²=144 in² (12²), not just 12 in²—to accurately transform square measurements.
Key Concepts
Property To convert units of area, you must convert the units for both length and width. This requires multiplying by the unit ratio twice, once for each dimension. You can also square the unit ratio before multiplying. $$ \left(\frac{3 \text{ ft}}{1 \text{ yd}}\right)^2 = \frac{9 \text{ ft}^2}{1 \text{ yd}^2} $$.
Examples Convert 10 square feet to square inches: $10 \text{ ft}^2 \cdot \left(\frac{12 \text{ in}}{1 \text{ ft}}\right)^2 = 10 \text{ ft}^2 \cdot \frac{144 \text{ in}^2}{1 \text{ ft}^2} = 1440 \text{ in}^2$.
Convert 5 square meters to square centimeters: $5 \text{ m}^2 \cdot \left(\frac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 5 \text{ m}^2 \cdot \frac{10000 \text{ cm}^2}{1 \text{ m}^2} = 50000 \text{ cm}^2$.
Common Questions
Why do you square the conversion factor when converting units of area?
Area is measured in square units (two dimensions). When converting 1 ft to 12 inches, area conversion requires squaring: 1 ft² = (12 in)² = 144 in². The conversion factor must be applied twice, once for each dimension.
How do you convert 3 square yards to square feet?
Since 1 yard = 3 feet, then 1 yd² = (3 ft)² = 9 ft². Multiply: 3 yd² × 9 ft²/yd² = 27 ft². Always square the linear conversion factor first, then multiply by the given area.
What is the most common mistake when converting area units?
Students often multiply by the linear conversion factor instead of its square. For example, incorrectly converting 2 ft² to inches by multiplying by 12 to get 24 in² instead of multiplying by 144 to get 288 in².