Question

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)
Responses

162 yd2
162 yd2

198 yd2
198 yd2

18 yd2
18 yd2

180 yd2

Answer 1

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

1. **Calculate the area of the goat's fenced area**:
\[
\text{Area}_{\text{goats}} = \text{length} \times \text{width} = 12 \, \text{yd} \times 15 \, \text{yd} = 180 \, \text{yd}^2
\]

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

3. **Calculate the area where the goats can roam**:
\[
\text{Area}_{\text{roaming}} = \text{Area}_{\text{goats}} - \text{Area}_{\text{garden}} = 180 \, \text{yd}^2 - 18 \, \text{yd}^2 = 162 \, \text{yd}^2
\]

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