Question

Jasmine wants to make a path from one corner of her yard to the other as shown. The path will be 3 feet wide. What is the area of the path?

A rectangle has a height of 30 feet and a base of 12 feet. A 3 feet wide path forms a parallelogram inside of the rectangle.

sq ft

Answer 1

To find the area of the path Jasmine wants to create, we first need to calculate the area of the rectangle and then the area of the inner parallelogram formed by the path.

1. **Calculate the area of the rectangle:**
\[
\text{Area of the rectangle} = \text{base} \times \text{height} = 12 \, \text{ft} \times 30 \, \text{ft} = 360 \, \text{sq ft}
\]

2. **Calculate the dimensions of the inner parallelogram (the area that stays inside the path):**
Since the path is 3 feet wide all around, we will subtract 3 feet from each side of the rectangle to find the dimensions of the inner parallelogram:
- New base = \( 12 \, \text{ft} - 2 \times 3 \, \text{ft} = 6 \, \text{ft} \)
- New height = \( 30 \, \text{ft} - 2 \times 3 \, \text{ft} = 24 \, \text{ft} \)

3. **Calculate the area of the inner parallelogram:**
\[
\text{Area of the inner parallelogram} = \text{new base} \times \text{new height} = 6 \, \text{ft} \times 24 \, \text{ft} = 144 \, \text{sq ft}
\]

4. **Calculate the area of the path:**
The area of the path is the area of the rectangle minus the area of the inner parallelogram:
\[
\text{Area of the path} = \text{Area of the rectangle} - \text{Area of the inner parallelogram} = 360 \, \text{sq ft} - 144 \, \text{sq ft} = 216 \, \text{sq ft}
\]

Therefore, the area of the path is \( \boxed{216} \) square feet.