A farmer wants to create a rectangular fence for his goats that is 12 yd. by 15 yd. Inside the same area, the farmer will also build a small rectangular fenced garden that is 3 yd. by 6 yd. If the goats are not allowed in the garden, how many square yards is the fenced area that the goats will be allowed to roam in?(1 point)

Question

Responses

18 yd2
18 yd2

198 yd2
198 yd2

180 yd2
180 yd2

162 yd2

Answer 1

To find the area where the goats will be allowed to roam, we need to calculate the total area of the larger fenced area and then subtract the area of the garden that is fenced off.

1. Calculate the area of the goat fence: \[ \text{Area of goat fence} = \text{length} \times \text{width} = 12 , \text{yd} \times 15 , \text{yd} = 180 , \text{yd}^2 \]

2. Calculate the area of the garden: \[ \text{Area of garden} = \text{length} \times \text{width} = 3 , \text{yd} \times 6 , \text{yd} = 18 , \text{yd}^2 \]

3. Subtract the area of the garden from the area of the goat fence: \[ \text{Area for goats} = \text{Area of goat fence} - \text{Area of garden} = 180 , \text{yd}^2 - 18 , \text{yd}^2 = 162 , \text{yd}^2 \]

Therefore, the area that the goats will be allowed to roam is 162 yd².