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 smaller garden, how many square yards is the fenced area that the goats will be allowed to roam in? (1 point)

Question

Responses

152 yd2
2
152 yd2

52 yd2
2
52 yd2

62 yd2
2
62 yd2

162 yd2

Answer 1

To find the area that the goats will be allowed to roam in, we first calculate the total area of the larger fenced area and then subtract the area of the smaller garden.

1. Calculate the area of the larger fenced area for the goats: \[ \text{Area of larger fenced area} = 12 , \text{yd} \times 15 , \text{yd} = 180 , \text{yd}^2 \]

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

3. Now, subtract the area of the garden from the area of the fenced area for the goats: \[ \text{Area for goats} = \text{Area of larger fenced area} - \text{Area of smaller garden} = 180 , \text{yd}^2 - 18 , \text{yd}^2 = 162 , \text{yd}^2 \]

So the area that the goats will be allowed to roam in is 162 yd².