To find the surface area of a right rectangular prism, you need to calculate the area of all six faces of the prism and then sum them up. A right rectangular prism has three pairs of identical faces.

Let's break down the process:

1. Identify the dimensions of the prism:

   • Let $l$ be the length.
   • Let $w$ be the width.
   • Let $h$ be the height.

2. Formula for the surface area: The surface area $A$ of a right rectangular prism is given by the formula: $A = 2lw + 2lh + 2wh$ This accounts for the areas of the three pairs of identical faces.

3. Detailed Calculation:

   • The area of the two faces with dimensions $l \times w$ is $2lw$.
   • The area of the two faces with dimensions $l \times h$ is $2lh$.
   • The area of the two faces with dimensions $w \times h$ is $2wh$.

   Therefore, the total surface area $A$ is: $A = 2lw + 2lh + 2wh$

4. Example Calculation: Suppose the dimensions of the prism are:

   • Length ($l$) = 5 units
   • Width ($w$) = 3 units
   • Height ($h$) = 4 units

   Plug these values into the formula: $A = 2(5 \times 3) + 2(5 \times 4) + 2(3 \times 4)$ $A = 2(15) + 2(20) + 2(12)$ $A = 30 + 40 + 24 = 94 \text{ square units}$

   So, the surface area of this right rectangular prism is 94 square units.

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:

1. How does the surface area change if one of the dimensions doubles?
2. What is the surface area if the dimensions are all equal (i.e., a cube)?
3. How do you find the volume of a right rectangular prism?
4. What happens to the surface area if only the height is tripled?
5. Can you derive the formula for the surface area of a prism from the general shape of the faces?

Tip: Always double-check the units of your measurements to ensure consistency when calculating surface areas.