To estimate the cost of having a 13 ft by 21 ft brick patio installed, let's first calculate the cost per square foot based on the 15 ft by 20 ft patio:

1. Area of the original patio (15 ft by 20 ft): $15 \times 20 = 300 \, \text{square feet}$

2. Cost per square foot: $\frac{2275}{300} \approx 7.58 \, \text{dollars per square foot}$

3. Area of the new patio (13 ft by 21 ft): $13 \times 21 = 273 \, \text{square feet}$

4. Estimated cost for the new patio: $273 \times 7.58 \approx 2,070.34 \, \text{dollars}$

So, the estimated cost for installing a 13 ft by 21 ft brick patio would be approximately $2,070.34.

Would you like more details on any part of this solution? Here are five related questions to consider:

1. What factors influence the cost per square foot of patio installation?
2. How do different materials (e.g., pavers vs. bricks) affect the overall cost?
3. How does labor pricing vary in different regions for patio installation?
4. What additional costs might arise during patio installation?
5. What are alternative methods to calculate installation costs more precisely?

Tip: Always factor in possible hidden costs, such as site preparation or additional materials, when estimating large projects.