To find the area of the region that is to be seeded with grass, we can break this problem into a few steps:

Step 1: Calculate the area of the entire backyard.

The backyard is a rectangle with dimensions 14 meters by 28 meters.

$\text{Area of the backyard} = \text{length} \times \text{width} = 14 \, \text{m} \times 28 \, \text{m} = 392 \, \text{m}^2$

Step 2: Calculate the area of the patio.

The patio is a square with side length 7 meters.

$\text{Area of the patio} = \text{side}^2 = 7 \, \text{m} \times 7 \, \text{m} = 49 \, \text{m}^2$

Step 3: Calculate the area of the flower garden.

The flower garden is a square with side length 2 meters.

$\text{Area of the garden} = \text{side}^2 = 2 \, \text{m} \times 2 \, \text{m} = 4 \, \text{m}^2$

Step 4: Calculate the area to be seeded with grass.

The total area that is to be seeded with grass is the area of the backyard minus the areas of the patio and the garden.

$\text{Area to be seeded} = \text{Area of the backyard} - \text{Area of the patio} - \text{Area of the garden}$

Substituting the values:

$\text{Area to be seeded} = 392 \, \text{m}^2 - 49 \, \text{m}^2 - 4 \, \text{m}^2 = 339 \, \text{m}^2$

Final Answer:

The area of the region that is to be seeded with grass is 339 square meters.

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Would you like any further details or clarifications?

Here are 5 related questions:

1. How would the area change if the patio were circular?
2. What if the garden had a different shape, like a triangle?
3. Can you find the percentage of the backyard covered by the patio and garden?
4. How would you calculate the area if the dimensions were given in feet?
5. What if there were multiple gardens of different sizes?

Tip: Always subtract areas of objects that won't be included in the final surface, such as patios or flower beds, from the total area when calculating land coverage!