1. **State the problem:** We have two similar trapezoids, Shape A and Shape B. Given dimensions: - Shape A: top = 4 cm, right side = 12 cm, bottom-left side = 7 cm - Shape B: top = 3 cm, right side = 9 cm, bottom-left side = w cm We need to find: a) The scale factor from Shape A to Shape B. b) The value of w. 2. **Calculate the scale factor (a):** For similar shapes, corresponding sides are proportional. Using the top sides: $$a = \frac{\text{top side of B}}{\text{top side of A}} = \frac{3}{4}$$ Using the right sides: $$a = \frac{9}{12} = \frac{3}{4}$$ Since both ratios match, the scale factor from A to B is $\frac{3}{4}$. 3. **Find the value of w:** Since sides correspond and scale by $\frac{3}{4}$, the bottom-left side scales same way. $$w = \frac{3}{4} \times 7 = \frac{21}{4}$$ 4. **Simplify the fraction:** $\frac{21}{4}$ is already in simplest form. **Final answers:** a) Scale factor = $\frac{3}{4}$ b) $w = \frac{21}{4}$