Questions: A rectangular yard measuring 27 ft by 43 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.

Solution Steps

To find the area of the walk, we need to calculate the area of the entire yard including the walk and then subtract the area of the yard without the walk. The walk is 2 ft wide and goes all the way around the yard.

1. Calculate the dimensions of the yard including the walk.
2. Calculate the area of the yard including the walk.
3. Calculate the area of the yard without the walk.
4. Subtract the area of the yard without the walk from the area of the yard including the walk to get the area of the walk.

The yard has dimensions \(27 \, \text{ft} \times 43 \, \text{ft}\). The walk is 2 ft wide and goes all the way around the yard. Therefore, the dimensions of the yard including the walk are: \[ \text{Length with walk} = 27 + 2 \times 2 = 31 \, \text{ft} \] \[ \text{Width with walk} = 43 + 2 \times 2 = 47 \, \text{ft} \]

The area of the yard including the walk is: \[ \text{Area with walk} = 31 \times 47 = 1457 \, \text{ft}^2 \]

The area of the yard without the walk is: \[ \text{Area of yard} = 27 \times 43 = 1161 \, \text{ft}^2 \]

The area of the walk is the difference between the area of the yard including the walk and the area of the yard without the walk: \[ \text{Area of walk} = 1457 - 1161 = 296 \, \text{ft}^2 \]

Final Answer