Question

a rectangular garden measures 31 ft by 39 ft. surrounding (and bordering) the garden is a path 3 ft wide. find the area of this path. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the larger rectangle (garden + path)

The formula for the area of a rectangle is \(A = l\times w\). The length of the larger rectangle is \(31 + 2\times3=31 + 6 = 37\) ft (adding 3 ft on each side for the path), and the width of the larger rectangle is \(39+ 2\times3=39 + 6=45\) ft. So the area of the larger rectangle \(A_{1}=37\times45=\$1665\) \(ft^{2}\).

Step2: Calculate the area of the garden

The area of the garden \(A_{2}=31\times39 = 1209\) \(ft^{2}\).

Step3: Calculate the area of the path

The area of the path \(A=A_{1}-A_{2}\). Substitute the values: \(A = 1665-1209=456\) \(ft^{2}\).

Answer:

456 \(ft^{2}\)