Let's solve the problem from the image.

Problem 1: Calculate the area for grass replacement.

The diagram shows an "L"-shaped figure with the following dimensions:

• The top horizontal part is 7 feet by 7 feet.
• The vertical part is 14 feet long and 7 feet wide.

To find the area that needs to be covered with grass, we can break down the "L" shape into two rectangles and calculate their areas separately.

1. Top rectangle: $\text{Area} = 7 \, \text{feet} \times 7 \, \text{feet} = 49 \, \text{square feet}$

2. Bottom rectangle: $\text{Area} = 7 \, \text{feet} \times 14 \, \text{feet} = 98 \, \text{square feet}$

Finally, add the areas of both rectangles: $\text{Total Area} = 49 \, \text{square feet} + 98 \, \text{square feet} = 147 \, \text{square feet}$ So, 147 square feet of grass will be needed.

Problem 2: Calculate the length of wooden railing needed.

The wooden railing surrounds the entire "L" shape. We need to find the perimeter of the shape.

1. Perimeter of the top rectangle:

   • 7 feet (top) + 7 feet (bottom) = 14 feet (horizontal sides)
   • 7 feet (left) + 7 feet (right) = 14 feet (vertical sides)

2. Perimeter of the bottom rectangle:

   • 14 feet (vertical side)

Now, sum the lengths: $\text{Total Perimeter} = 7 + 7 + 14 + 14 + 7 = 49 \, \text{feet}$ So, 49 feet of wooden railing will be needed.

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Do you want further details or have any questions? Here are some related questions you might consider:

1. How would the calculations change if the shape was reversed?
2. Can you express the perimeter formula for any "L" shaped object?
3. How would the area calculation change if the widths of the rectangles were different?
4. How does changing the length of one side affect the total area?
5. What would be the effect of rounding errors on the total grass area?
6. If the entire shape was to be scaled by a factor of 2, what would the new area and perimeter be?
7. How could we apply these calculations to a real-life mini-golf course renovation project?
8. How would the railing calculation differ if the wooden railing also covered the interior corner of the "L"?

Tip: Always double-check your measurements when dealing with composite shapes to ensure accuracy in both area and perimeter calculations.