Question

a rectangular garden measures 31 ft by 56 ft. surrounding (and bordering) the garden is a path 4 ft wide. find the area of this path. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the outer rectangle's dimensions

The width of the outer rectangle is \(31 + 4+4=39\) ft (adding 4 ft on each side).
The length of the outer rectangle is \(56 + 4 + 4=64\) ft (adding 4 ft on each side).

Step2: Calculate the areas of the outer and inner rectangles

The area of a rectangle is \(A = length\times width\).
The area of the outer rectangle \(A_{outer}=39\times64 = 2496\) \(ft^{2}\).
The area of the inner (garden) rectangle \(A_{inner}=31\times56=1736\) \(ft^{2}\).

Step3: Calculate the area of the path

The area of the path is \(A = A_{outer}-A_{inner}\).
\(A=2496 - 1736=760\) \(ft^{2}\).

Answer:

\(760\) \(ft^{2}\)