Question

a rectangular yard measuring 33 ft by 51 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 outer - rectangle area

The outer - rectangle (yard) has dimensions 33 ft by 51 ft. The area formula for a rectangle is $A = l\times w$. So, $A_{outer}=33\times51 = 1683$ square feet.

Step2: Calculate inner - rectangle dimensions

Since the walk is 2 ft wide all around, the length of the inner - rectangle is $l_{inner}=33-(2 + 2)=29$ ft and the width of the inner - rectangle is $w_{inner}=51-(2 + 2)=47$ ft.

Step3: Calculate inner - rectangle area

Using the area formula $A = l\times w$ again, $A_{inner}=29\times47=1363$ square feet.

Step4: Calculate walk area

The area of the walk is the difference between the outer - rectangle area and the inner - rectangle area. So, $A = A_{outer}-A_{inner}=1683 - 1363=320$ square feet.

Answer:

320 ft²