Surface Area Comparison: 1x2x3 vs 2x1x3 Rectangular Prisms

To solve the problem, we'll proceed through these steps:

• Step 1: Identify the dimensions of the orthohedrons from the diagram.
• Step 2: Apply the surface area formula for a cuboid.
• Step 3: Compare the surface areas to determine if they are equal or different.

Step 1: Dimensions from the diagram:

• Orthohedron 1: Length $l = 3$, Width $w = 2$, Height $h = 1$.
• Orthohedron 2: Length $l = 2$, Width $w = 3$, Height $h = 1$.

Step 2: Calculate surface areas using the formula $SA = 2(lw + lh + wh)$.

For Orthohedron 1:
$SA_1 = 2(3 \cdot 2 + 3 \cdot 1 + 2 \cdot 1) = 2(6 + 3 + 2) = 2(11) = 22$.

For Orthohedron 2:
$SA_2 = 2(2 \cdot 3 + 2 \cdot 1 + 3 \cdot 1) = 2(6 + 2 + 3) = 2(11) = 22$.

Step 3: Compare the surface areas:
Both orthohedrons have a surface area of 22; therefore, the surface areas are equal.

Thus, the surface areas of the two orthohedrons are equal.

The correct answer is: $=$.