Question

1. a rectangle is 8 feet long and 4 feet wide. if we remove a 2 square out of one corner of the rectangle, how many square inches would remain in the rectangle?

Explanation:

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<reasoning>

Calculate the remaining area in square feet

\[

$$\begin{aligned} A_{\text{rectangle}} &= 8\text{ ft} \times 4\text{ ft} = 32\text{ sq ft} \\ A_{\text{square}} &= 2\text{ ft} \times 2\text{ ft} = 4\text{ sq ft} \\ A_{\text{remaining, sq ft}} &= 32\text{ sq ft} - 4\text{ sq ft} = 28\text{ sq ft} \end{aligned}$$

\]

Convert the remaining area to square inches

\[

$$\begin{aligned} 1\text{ sq ft} &= 12\text{ in} \times 12\text{ in} = 144\text{ sq in} \\ A_{\text{remaining, sq in}} &= 28 \times 144 = 4032\text{ sq in} \end{aligned}$$

\]
</reasoning>

<answer>
\(4032\text{ square inches}\)
</answer>

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Answer:

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<reasoning>

Calculate the remaining area in square feet

\[

$$\begin{aligned} A_{\text{rectangle}} &= 8\text{ ft} \times 4\text{ ft} = 32\text{ sq ft} \\ A_{\text{square}} &= 2\text{ ft} \times 2\text{ ft} = 4\text{ sq ft} \\ A_{\text{remaining, sq ft}} &= 32\text{ sq ft} - 4\text{ sq ft} = 28\text{ sq ft} \end{aligned}$$

\]

Convert the remaining area to square inches

\[

$$\begin{aligned} 1\text{ sq ft} &= 12\text{ in} \times 12\text{ in} = 144\text{ sq in} \\ A_{\text{remaining, sq in}} &= 28 \times 144 = 4032\text{ sq in} \end{aligned}$$

\]
</reasoning>

<answer>
\(4032\text{ square inches}\)
</answer>

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