Question

We have a shape that has an area of 112 inches squared. Convert the units to centimeters squared. (HINT: Perform multiple conversions). Don’t forget to show your work.

Answer 1

Answer: 722.5792 square centimeters

Work Shown:

$112 \text{ in}^2 = 112 \text{ in}^2 \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\\\\112 \text{ in}^2 = (112 \times 2.54 \times 2.54) \text{ cm}^2\\\\112 \text{ in}^2 = 112 \times (2.54)^2 \text{ cm}^2\\\\112 \text{ in}^2 = 722.5792 \text{ cm}^2$

Notes:

• 1 inch = 2.54 cm exactly
• The conversion factor $\frac{2.54 \text{ cm}}{1 \text{ in}}$ is used to convert from inches to cm. The inches unit in the denominator cancels with one of the inches unit from the original 112 square inches figure.
• We use two identical copies of the same conversion factor to convert from square inches to square centimeters. This is the "multple conversion" your teacher is referring to.
• Think of "square inches", aka $\text{in}^2$, as "inches times inches". Or think of a 1 inch by 1 inch square that has an area of 1 square inch. The same applies for the square centimeter unit as well.