1. **State the problem:** Find the surface area of a set of three steps with dimensions: height of smallest step = 16 cm, depth of top step = 25 cm, total depth = 90 cm. 2. **Understand the shape:** The steps form a stair-like shape with three rectangular steps rising from front to back. 3. **Identify dimensions:** - Height of each step: 16 cm - Depth of top step: 25 cm - Total depth: 90 cm 4. **Calculate depth of each step:** Since total depth is 90 cm and top step depth is 25 cm, the remaining depth is 90 - 25 = 65 cm. Assuming equal depth for the other two steps, each has depth $\frac{65}{2} = 32.5$ cm. 5. **Calculate surface area:** Surface area includes: - Top surfaces of all steps - Front vertical faces of all steps - Side faces (assuming width is constant but not given, so we consider only given dimensions) 6. **Calculate top surface area:** - Top step: $25 \times \text{width}$ - Middle step: $32.5 \times \text{width}$ - Bottom step: $32.5 \times \text{width}$ Since width is not given, assume width = 1 cm for calculation of relative surface area. Top surface area = $25 \times 1 + 32.5 \times 1 + 32.5 \times 1 = 90$ cm$^2$. 7. **Calculate front vertical faces:** Each step has a front face of height 16 cm and width 1 cm. Number of steps = 3 Total front area = $3 \times 16 \times 1 = 48$ cm$^2$. 8. **Calculate side faces:** Two side faces, each with height total $3 \times 16 = 48$ cm and depth 90 cm. Side area = $2 \times 48 \times 1 = 96$ cm$^2$. 9. **Calculate bottom face:** Bottom face area = depth $90$ cm $\times$ width $1$ cm = 90 cm$^2$. 10. **Sum all areas:** Total surface area = top surfaces + front faces + side faces + bottom face = $90 + 48 + 96 + 90 = 324$ cm$^2$. **Final answer:** The surface area of the set of steps is $324$ cm$^2$.