Question

a rectangular yard measuring 27 ft by 32 ft is bordered (and surrounded) by a fence. inside, a walk that is 2 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 outer rectangle area

The formula for the area of a rectangle is \(A = l\times w\). The outer length \(l_{outer}=32 + 2+2=36\) ft (adding 2 ft on each side for the walk), and the outer width \(w_{outer}=27 + 2+2 = 31\) ft. So, \(A_{outer}=36\times31\)

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Step2: Calculate the inner rectangle area

The inner length \(l_{inner}=32\) ft and the inner width \(w_{inner}=27\) ft. So, \(A_{inner}=32\times27=(30 + 2)\times27=30\times27+2\times27=810 + 54=864\)

Step3: Calculate the walk area

The area of the walk \(A = A_{outer}-A_{inner}\). So, \(A=1116-864 = 252\)

Answer:

\(252\mathrm{ft}^{2}\)