1. Problem 10: Calculate the area in square feet of a horse stable from a scale drawing.
- Given scale: 1 inch = $3^2 = 9$ feet.
- Drawing dimensions: 15 inches by 30 inches.
2. Formula for actual length: Actual length = Drawing length $\times$ scale factor.
3. Calculate actual dimensions:
- Actual length = $15 \times 9 = 135$ feet.
- Actual width = $30 \times 9 = 270$ feet.
4. Calculate area in square feet:
$$\text{Area} = 135 \times 270 = 36450 \text{ square feet}$$
---
5. Problem 11: Find the area of a rectangle after enlargement by a scale factor squared.
- Original rectangle dimensions: 9 cm by 5 cm.
- Scale factor: $2.5$.
6. Area of original rectangle:
$$9 \times 5 = 45 \text{ cm}^2$$
7. Area scale factor is the square of the linear scale factor:
$$2.5^2 = 6.25$$
8. Calculate new area:
$$45 \times 6.25 = 281.25 \text{ cm}^2$$
---
9. Problem 12: Find the area of a parallelogram after enlargement by a scale factor squared.
- Original parallelogram base = 6 cm, height = 6 cm.
- Scale factor: $2.2$.
10. Area of original parallelogram:
$$6 \times 6 = 36 \text{ cm}^2$$
11. Area scale factor:
$$2.2^2 = 4.84$$
12. Calculate new area:
$$36 \times 4.84 = 174.24 \text{ cm}^2$$
---
Final answers:
- Problem 10: $36450$ square feet.
- Problem 11: $281.25$ square centimeters.
- Problem 12: $174.24$ square centimeters.
Area Scale
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.