To determine which option has the maximum shaded area, we will calculate the area for each of the given figures step by step.
### Step 1: Analyze Option 1
- **Identify the dimensions of the rectangles**:
- The first rectangle has dimensions of 8 meters (length) and 1 meter (width).
- The second rectangle has dimensions of 2 meters (length) and 10 meters (width).
- **Calculate the area of the first rectangle**:
\[
\text{Area}_1 = \text{length} \times \text{width} = 8 \, \text{m} \times 1 \, \text{m} = 8 \, \text{m}^2
\]
- **Calculate the area of the second rectangle**:
\[
\text{Area}_2 = \text{length} \times \text{width} = 2 \, \text{m} \times 10 \, \text{m} = 20 \, \text{m}^2
\]
- **Total area of Option 1**:
\[
\text{Total Area}_1 = \text{Area}_1 + \text{Area}_2 = 8 \, \text{m}^2 + 20 \, \text{m}^2 = 28 \, \text{m}^2
\]
### Step 2: Analyze Option 2
- **Identify the dimensions of the rectangles**:
- The first rectangle has dimensions of 9 meters (length) and 1 meter (width).
- The second rectangle has dimensions of 2 meters (length) and 10 meters (width).
- **Calculate the area of the first rectangle**:
\[
\text{Area}_1 = \text{length} \times \text{width} = 9 \, \text{m} \times 1 \, \text{m} = 9 \, \text{m}^2
\]
- **Calculate the area of the second rectangle**:
\[
\text{Area}_2 = \text{length} \times \text{width} = 2 \, \text{m} \times 10 \, \text{m} = 20 \, \text{m}^2
\]
- **Total area of Option 2**:
\[
\text{Total Area}_2 = \text{Area}_1 + \text{Area}_2 = 9 \, \text{m}^2 + 20 \, \text{m}^2 = 29 \, \text{m}^2
\]
### Step 3: Analyze Option 3
- **Identify the dimensions of the rectangles**:
- The outer rectangle has dimensions of 12 meters (length) and 10 meters (width).
- The inner rectangle has dimensions of 7.5 meters (length) and 2 meters (width).
- **Calculate the area of the outer rectangle**:
\[
\text{Area}_{\text{outer}} = \text{length} \times \text{width} = 12 \, \text{m} \times 10 \, \text{m} = 120 \, \text{m}^2
\]
- **Calculate the area of the inner rectangle**:
\[
\text{Area}_{\text{inner}} = \text{length} \times \text{width} = 7.5 \, \text{m} \times 2 \, \text{m} = 15 \, \text{m}^2
\]
- **Total shaded area of Option 3**:
\[
\text{Shaded Area}_3 = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 120 \, \text{m}^2 - 15 \, \text{m}^2 = 105 \, \text{m}^2
\]
### Conclusion
After calculating the total shaded areas for each option:
- Option 1: 28 m²
- Option 2: 29 m²
- Option 3: 105 m²
**The option with the maximum shaded area is Option 3 with an area of 105 m².**
