The given image shows a coordinate grid with Derek's house and play area. The play area needs to be fenced, and each unit on the grid represents 5 feet. The cost for fencing is $10 per foot.

Steps to solve:

1. Determine the dimensions of the play area:

   • From the grid, we count the number of units along the sides that require fencing. Let's label them.
     • The bottom side of the play area (along the x-axis) has a length of 5 units.
     • The right side of the play area (along the y-axis) has a height of 3 units.

2. Convert units to feet:

   • Each unit on the grid represents 5 feet.
     • Bottom side: $5 \text{ units} \times 5 \text{ feet/unit} = 25 \text{ feet}$
     • Right side: $3 \text{ units} \times 5 \text{ feet/unit} = 15 \text{ feet}$

3. Calculate the total length of the fence:

   • Only the bottom, right, and bottom left sections of the play area need fencing since part of the play area is shared with the house.
   • Total fencing needed: $\text{Total length} = 25 \text{ feet (bottom)} + 15 \text{ feet (right)} + 15 \text{ feet (left)} = 55 \text{ feet}$

4. Calculate the total cost:

   • Cost per foot of fencing is $10. $\text{Total cost} = 55 \text{ feet} \times 10 \text{ dollars/foot} = 550 \text{ dollars}$

Thus, it will cost $550 to install the fence.

Would you like more details on this solution or have any questions?

Here are 5 questions to consider:

1. What would happen if Derek needed to fence all four sides of the play area?
2. How would the cost change if the price per foot of fencing increased to $12 per foot?
3. What is the perimeter of the play area if the house were not attached?
4. How much more would the cost be if the play area were expanded by 2 units in length?
5. Could Derek reduce the cost by adjusting the dimensions of the play area?

Tip: Always double-check units when converting from grids to real-world measurements to ensure accuracy!