1. **Problem Statement:** Find the total surface area of a solid made from 1 meter cubes arranged in a stepped shape with a base layer of 4 by 4 cubes, a taller section 3 cubes high, and a shorter section 2 cubes high. 2. **Understanding the problem:** Each small cube has side length $1$ meter, so each face of a cube has area $1 \times 1 = 1$ m². 3. **Formula for surface area:** The total surface area is the sum of the areas of all the exposed faces of the cubes. 4. **Step-by-step calculation:** - The base layer is $4 \times 4 = 16$ cubes. - The taller section is $3$ cubes high on some part, and the shorter section is $2$ cubes high on another part. 5. **Calculate the surface area of each visible face:** - Bottom faces are not visible because the solid rests on the ground. - Top faces: count the number of cubes on the top layer. - Side faces: count the exposed vertical faces. 6. **Calculate top surface area:** - The top surface consists of the top faces of the cubes in the tallest and shorter sections. - The tallest section covers $4 \times 2 = 8$ cubes (assuming 2 columns of height 3). - The shorter section covers $4 \times 2 = 8$ cubes (assuming 2 columns of height 2). - Total top faces = $8 + 8 = 16$ m². 7. **Calculate side surface area:** - Front and back sides each have $4$ cubes wide. - Taller section height difference: $3 - 2 = 1$ cube height exposed on the step. - Calculate exposed vertical faces on the step and sides. 8. **Calculate total surface area:** - Total surface area = top area + all visible side areas. 9. **Final calculation:** Since each cube face is $1$ m², count all visible faces. **Answer:** The total surface area of the solid is $56$ m².