1. The problem involves finding the areas of two rectangles given their dimensions. 2. The formula for the area of a rectangle is $$\text{Area} = \text{width} \times \text{height}$$. 3. For the green rectangle (top-left), the width is $6b$ cm and the height is $\frac{1}{2}a$ cm. 4. Calculate the area of the green rectangle: $$\text{Area}_{green} = 6b \times \frac{1}{2}a = 3ab$$ cm$^2$. 5. For the orange rectangle (top-right), the width is $7c$ cm and the height is $\frac{3}{5}d$ cm. 6. Calculate the area of the orange rectangle: $$\text{Area}_{orange} = 7c \times \frac{3}{5}d = \frac{21}{5}cd$$ cm$^2$. 7. These expressions give the areas of the two rectangles in terms of the variables $a$, $b$, $c$, and $d$. Final answers: - Green rectangle area: $3ab$ cm$^2$ - Orange rectangle area: $\frac{21}{5}cd$ cm$^2$