Pregunta
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A rectangular window is 3 ft long and 2 ft wide. Karen would like to buy a screen for the window. The cost of the screen is based on the number of square inches th screen is. Use the facts to find the area of the window square inches.

Ask by Cole Ball. in the United States
Jan 23,2025

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The area of the window is 864 square inches.

Solución

To determine the area of Karen's rectangular window in square inches, follow these steps: ### 1. Convert Measurements from Feet to Inches Since the window dimensions are given in feet, and the final area needs to be in square inches, we first convert each measurement from feet to inches. - **Length conversion:** \[ 3 \text{ feet} \times 12 \frac{\text{inches}}{\text{foot}} = 36 \text{ inches} \] - **Width conversion:** \[ 2 \text{ feet} \times 12 \frac{\text{inches}}{\text{foot}} = 24 \text{ inches} \] ### 2. Calculate the Area in Square Inches Now, use the converted measurements to find the area of the rectangle. \[ \text{Area} = \text{Length} \times \text{Width} = 36 \text{ inches} \times 24 \text{ inches} = 864 \text{ square inches} \] ### **Conclusion** The area of Karen's window is **864 square inches**. This means the cost of the screen will be based on this area measurement.

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The Deep Dive

To find the area of the window in square inches, first calculate the area in square feet. The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). In this case, the area in square feet is \( 3 \, \text{ft} \times 2 \, \text{ft} = 6 \, \text{sq ft} \). Since there are 144 square inches in a square foot (12 in x 12 in), multiply the area in square feet by 144 to convert it to square inches: \( 6 \, \text{sq ft} \times 144 \, \text{in}^2/\text{sq ft} = 864 \, \text{sq in} \). If Karen wants to avoid accidental costs when ordering her screen, she's got to double-check her measurements! Measure the window a second time, ideally using the same measuring tape, just to ensure accuracy. Overestimating could lead to buying too much material, while underestimating can result in extra trips to the store – which nobody enjoys!

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