Skill: Find surface area of rectangular prisms

Surface area is the total area covering the outside of a rectangular prism. A rectangular prism has three pairs of matching rectangular faces:

• length $\times$ width: $lw$
• length $\times$ height: $lh$
• width $\times$ height: $wh$

Because each face has a matching face, use:

$$\text{Surface area}=2(lw+lh+wh)$$

Example

Find the surface area of a rectangular prism with length $5$ cm, width $3$ cm, and height $2$ cm.

Step 1: Identify the dimensions.

$$l=5,\qquad w=3,\qquad h=2$$

Step 2: Find the areas of the three different faces.

$$lw=5\cdot3=15$$ $$lh=5\cdot2=10$$ $$wh=3\cdot2=6$$

Step 3: Add these areas and multiply by $2$.

$$\text{Surface area}=2(15+10+6)$$ $$=2(31)=62$$

Step 4: Write the answer in square units.

$$\boxed{62\text{ cm}^2}$$

The surface area is $62\text{ cm}^2$. Remember, surface area measures the outside faces, while volume measures the space inside the prism.