Andrea was given a problem about the area of a rectangle. Her teacher asked her to see what the area would be if the width of the rectangle is a 4 -foot log and the length is made of two logs pushed together, a 2 -foot log and a 1 -foot log. She couldn't see how to do the computation because she knew the area had to be in square feet. She got 4 times 2 to be 8 square feet and 4 times 1 to be 4 feet. Andrea knew that they couldn't be the same units. How would you help her? Choose the correct answer below. A. She should have added instead of multiplied. The area is ( \( 4 \mathrm{ft}+2 \mathrm{ft})+(4 \mathrm{ft}+1 \mathrm{ft}) \), or 11 feet. B. She correctly found 4 ft times 1 ft to be 4 feet, but 4 ft times 2 ft is 8 feet. The area is 12 feet. C. She correctly found 4 ft times 2 ft to be 8 square feet, but 4 ft times 1 ft is 4 square feet. The area is 12 square feet. D. She should have added instead of multiplied. The area is \( (4 \mathrm{ft}+2 \mathrm{ft})+(4 \mathrm{ft}+1 \mathrm{ft}) \), or 11 square feet.
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To help Andrea clarify her confusion, it's essential to guide her on the correct way to calculate the area of a rectangle. The area formula is indeed length times width. In her case, the length made up of a 2-foot log and a 1-foot log should be added, giving her a total length of 3 feet. So she needs to multiply the width (4 feet) by the total length (3 feet) to get the area. That’s \( 4 \text{ ft} \times 3 \text{ ft} = 12 \text{ square feet} \)! Additionally, a common mistake students make is ignoring units when performing calculations. It's vital to keep track of whether you're adding or multiplying quantities. In this problem, since width and length are both in feet, multiplying them gives you square feet, which is the correct unit for area. So, by focusing on proper unit management, we can avoid confusion and ensure that Andrea learns from these helpful reminders!