1. **Stating the problem:** Calculate the area of the step-like composite polygon composed of rectangles with side lengths labeled as $a$, $b$, and $3a$. 2. **Understanding the shape:** The polygon is made of rectangular sections arranged in a step-like pattern. The side lengths given are $a$, $b$, and $3a$. 3. **Formula for area of rectangles:** The area of a rectangle is given by: $$\text{Area} = \text{length} \times \text{width}$$ 4. **Breaking down the polygon into rectangles:** - Bottom rectangle: dimensions $a \times b$ - Middle rectangle: dimensions $3a \times a$ - Top rectangle: dimensions $a \times b$ 5. **Calculating each area:** - Bottom rectangle area: $a \times b = ab$ - Middle rectangle area: $3a \times a = 3a^2$ - Top rectangle area: $a \times b = ab$ 6. **Summing the areas:** $$\text{Total area} = ab + 3a^2 + ab = 2ab + 3a^2$$ 7. **Final answer:** $$\boxed{2ab + 3a^2}$$ This is the total area of the step-like composite polygon.