Area & Perimeter A rectangle flower bed measures 10 ft by 6 ft. It has a path 2 ft around it. Draw a picture of this and find the area of the path.
a = [(10 + 4) * (6 + 4)] - (10 * 6)
To calculate the area of the path, we need to find the difference in area between the larger rectangle formed by the outer edges of the flower bed and the smaller rectangle formed by the inner edges of the flower bed (without the path).
First, let's draw a diagram to visualize the layout.
```
___________________
| |
| ______________ |
| | | |
| | | |
| | 10 ft | |
| | by | |
| | 6 ft | |
| | | |
| | | |
| |____________| |
| 2 ft |
|___________________|
```
In the diagram, the outer rectangle represents the flower bed including the path around it.
Now, we will calculate the area of the outer rectangle and the area of the inner rectangle.
The area of the outer rectangle is given by:
Area_outer = (10 ft + 2 ft + 2 ft) * (6 ft + 2 ft + 2 ft)
Area_outer = (14 ft) * (10 ft)
Area_outer = 140 ft²
The area of the inner rectangle (flower bed) is given by:
Area_inner = 10 ft * 6 ft
Area_inner = 60 ft²
Finally, we can find the area of the path by subtracting the area of the inner rectangle from the area of the outer rectangle:
Area_path = Area_outer - Area_inner
Area_path = 140 ft² - 60 ft²
Area_path = 80 ft²
Therefore, the area of the path is 80 square feet.
To draw a picture of the rectangle flower bed with a path around it, follow these steps:
1. Start by drawing a rectangle to represent the flower bed.
2. Label the length of the rectangle as 10 ft and the width as 6 ft.
3. Draw another rectangle around the first one, making sure to leave a 2 ft gap between the inner and outer rectangles.
4. Label the outer rectangle's length as 14 ft (10 ft + 2 ft + 2 ft) and the width as 10 ft (6 ft + 2 ft + 2 ft).
To find the area of the path, subtract the area of the inner rectangle (flower bed) from the area of the outer rectangle:
Area of the outer rectangle = length × width = 14 ft × 10 ft = 140 square feet
Area of the inner rectangle (flower bed) = length × width = 10 ft × 6 ft = 60 square feet
Area of the path = Area of the outer rectangle - Area of the inner rectangle
= 140 square feet - 60 square feet
= 80 square feet
So, the area of the path is 80 square feet.