Question

a rectangular yard measuring 38 ft by 67 ft is bordered (and surrounded) by a fence. inside, a walk that is 3 ft wide goes all the way along the fence. find the area of this walk. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the outer rectangle (yard + walk)

The formula for the area of a rectangle is \(A = l\times w\). The length of the outer rectangle \(l_{outer}=67 + 3+3=73\) ft (adding 3 ft on each side for the walk), and the width of the outer rectangle \(w_{outer}=38 + 3+3 = 44\) ft. So, \(A_{outer}=73\times44\).

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Step2: Calculate the area of the inner rectangle (yard only)

The length of the inner rectangle \(l_{inner}=67\) ft and the width \(w_{inner}=38\) ft. Using the area formula \(A = l\times w\), \(A_{inner}=67\times38\).

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Step3: Calculate the area of the walk

The area of the walk \(A_{walk}=A_{outer}-A_{inner}\). Substitute the values of \(A_{outer}\) and \(A_{inner}\): \(A_{walk}=3212-2546 = 666\) \(ft^{2}\)

Answer:

666 \(ft^{2}\)