Question

a rectangular yard measuring 36 ft by 61 ft is bordered (and surrounded) by a fence. inside, a walk that is 4 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: Determine the inner rectangle dimensions

The walk is 4 ft wide, so we subtract 2*4 ft from each dimension (4 ft from both sides) of the yard.
Length of inner rectangle: \( 61 - 2\times4 = 61 - 8 = 53 \) ft
Width of inner rectangle: \( 36 - 2\times4 = 36 - 8 = 28 \) ft

Step2: Calculate area of yard and inner rectangle

Area of yard (outer rectangle): \( 61\times36 = 2196 \) \( \text{ft}^2 \)
Area of inner rectangle (yard without walk): \( 53\times28 = 1484 \) \( \text{ft}^2 \)

Step3: Find area of the walk

Subtract inner area from outer area: \( 2196 - 1484 = 712 \) \( \text{ft}^2 \)

Answer:

\( 712 \) square feet (or \( 712\ \text{ft}^2 \))