https://file.aiquickdraw.com/mathbot/file/1729398399863pliy06u3.jpg

The problem involves finding the area of a path surrounding a rectangular field. Here's the breakdown:

### Step 1: Dimensions of the field
- The field itself is a rectangle measuring **20 meters by 12 meters**.

### Step 2: Dimensions of the outer rectangle (including the path)
- The path is **3 meters wide** around the entire field. This means the total length and width of the outer rectangle (field + path) are:
  - Length of the outer rectangle = \( 20 + 2 \times 3 = 26 \) meters
  - Width of the outer rectangle = \( 12 + 2 \times 3 = 18 \) meters

### Step 3: Areas
- **Area of the outer rectangle** (including the path) = \( 26 \times 18 = 468 \) square meters
- **Area of the field** (inner rectangle) = \( 20 \times 12 = 240 \) square meters

### Step 4: Area of the path
The area of the path is the difference between the area of the outer rectangle and the area of the field:
\[
\text{Area of the path} = 468 - 240 = 228 \, \text{square meters}
\]

Thus, the area of the path is **228 square meters**.

Would you like any more details or explanations? Here are some related questions:

1. How do we calculate the area of complex shapes?
2. How would the area change if the path width were different?
3. How do different units affect area calculation?
4. Can we calculate perimeter similarly to area?
5. How do we calculate the area for non-rectangular paths?

**Tip:** For problems involving surrounding areas like paths, always add the width of the path to both sides to find the dimensions of the outer shape.

The figure shows a rectangular field with a path 3 meters wide around it. Find the area of the path.

Learn how to calculate the area of a path surrounding a rectangular field. The field is 20 meters by 12 meters, and the path is 3 meters wide. This problem covers key geometric concepts and the formula for calculating the area of a rectangle, making it suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation