Let’s analyze the problem step by step using the diagram and questions provided in the image.

1. What is the area of the carrot section?

The carrot section is split into two vertical rectangular parts, each with dimensions $3\sqrt{3}$ feet by $\sqrt{3}$ feet.

• The area of each rectangle is: $A_{\text{carrot}} = 3\sqrt{3} \times \sqrt{3} = 3 \times 3 = 9 \text{ square feet}$

Since there are two carrot sections: $\text{Total area of carrot section} = 9 \times 2 = 18 \text{ square feet}$

2. What is the area of the radish section?

The radish section consists of four smaller squares, each with side lengths of $2\sqrt{3}$ feet.

• The area of each square is: $A_{\text{radish}} = (2\sqrt{3}) \times (2\sqrt{3}) = 4 \times 3 = 12 \text{ square feet}$

Thus, the total area of the radish section is 12 square feet.

3. What is the area of the lettuce section?

The lettuce section is a square with side lengths of $2\sqrt{3}$ feet.

• The area of the lettuce section is: $A_{\text{lettuce}} = (2\sqrt{3}) \times (2\sqrt{3}) = 4 \times 3 = 12 \text{ square feet}$

4. What area of the garden is not covered by carrots, lettuce, or radish?

First, find the total area of the square garden. The total side length of the garden is $3\sqrt{3}$ feet, so:

$\text{Total area of garden} = (3\sqrt{3}) \times (3\sqrt{3}) = 9 \times 3 = 27 \text{ square feet}$

Now, subtract the areas covered by the carrot, radish, and lettuce sections: $\text{Uncovered area} = 27 - (18 + 12 + 12) = 27 - 18 = 9 \text{ square feet}$

Thus, the area not covered by carrots, lettuce, or radish is 9 square feet.

Would you like further clarifications or details on any of these steps?

Here are 5 related questions to explore:

1. What is the total perimeter of the entire garden?
2. How would the areas change if the garden size increased by 50%?
3. What is the total area of all sections combined (carrot, radish, lettuce)?
4. What is the ratio of the carrot area to the radish area?
5. How much more area is covered by the carrots than by the lettuce?

Tip: When solving geometry problems, visualizing and labeling each section can make it easier to organize your calculations.