1. **Problem:** Ellie has a triangular island with an original area of 12 cm² using a wrong scale. The scale factor is enlarged to 3 cm. Find the new area. 2. **Formula:** Area scales by the square of the scale factor: $$\text{New Area} = \text{Original Area} \times (\text{Scale Factor})^2$$ 3. **Calculation:** - Original area = 12 cm² - Scale factor = 3 - New area = $$12 \times 3^2 = 12 \times 9 = 108 \text{ cm}^2$$ 4. **Answer:** The new area of the island is 108 cm². --- 1. **Problem:** Triangle B has dimensions twice those of triangle A. Area of B is 84 cm². Find area of A. 2. **Formula:** Area scales by the square of the scale factor: $$\text{Area}_B = \text{Area}_A \times (2)^2 = \text{Area}_A \times 4$$ 3. **Calculation:** - Given $$84 = 4 \times \text{Area}_A$$ - So, $$\text{Area}_A = \frac{84}{4} = 21 \text{ cm}^2$$ 4. **Answer:** Area of triangle A is 21 cm². --- 1. **Problem:** Triangles ABC and EFD are similar. Area of ABC is 81 units. Base ratio is $$\frac{8}{10} = \frac{2}{3}$$. Find area of EFD. 2. **Formula:** Area ratio = square of similarity ratio: $$\text{Area}_{EFD} = \text{Area}_{ABC} \times \left(\frac{2}{3}\right)^2 = 81 \times \frac{4}{9}$$ 3. **Calculation:** - $$81 \times \frac{4}{9} = 81 \times \frac{4}{9} = 9 \times 4 = 36$$ 4. **Answer:** Area of triangle EFD is 36 units². --- 1. **Problem:** Figure B and C are similar with scale factor 1:8. Area of C is 192 in². Find area of B. 2. **Formula:** Area scales by square of scale factor: $$\text{Area}_B = \text{Area}_C \times \left(\frac{1}{8}\right)^2 = 192 \times \frac{1}{64}$$ 3. **Calculation:** - $$192 \times \frac{1}{64} = 3$$ 4. **Answer:** Area of figure B is 3 in². --- 1. **Problem:** A rectangular garden is drawn with scale 1 inch = 30 yards. Drawing dimensions: 2 inches by 1.5 inches. Find actual area. 2. **Formula:** Actual length = drawing length × scale factor 3. **Calculation:** - Actual width = $$2 \times 30 = 60 \text{ yards}$$ - Actual height = $$1.5 \times 30 = 45 \text{ yards}$$ - Actual area = $$60 \times 45 = 2700 \text{ yards}^2$$ 4. **Answer:** Actual area of the garden is 2700 yards².