Comparing Surface Areas of Two Orthohedra: 1×2×3 Unit Analysis

To solve this problem, we'll follow these steps:

• Step 1: Determine the dimensions of each orthohedron from the diagram.
• Step 2: Calculate the surface area for each cuboid using the formula.
• Step 3: Compare the calculated surface areas.

Now, let's work through each step:

Step 1: Identify the Given Dimensions
From the visual data, we note that the dimensions of the first orthohedron are given as 1, 2, and 3, while the second orthohedron has the same visual size with similar digits 1, 2, and 3 marked, suggesting identical measurements for each dimension.

Step 2: Calculate the Surface Area for Each Cuboid
Utilize the surface area formula for cuboids:

$SA = 2(lw + lh + wh)$

For Both Orthohedra, Given Dimensions:

• Length ($l$): 1 unit
• Width ($w$): 2 units
• Height ($h$): 3 units

The surface area calculation will be:

$SA = 2(1 \cdot 2 + 1 \cdot 3 + 2 \cdot 3)$ $= 2(2 + 3 + 6)$ $= 2 \cdot 11$ $= 22 \text{ square units}$

As both cuboids have the same dimensions, their surface area calculations yield identical results.

Step 3: Compare Surface Areas
Since both orthohedra compute to the same total surface area of 22 square units, we conclude their surface areas are the same.

Therefore, the solution to the problem is The same.