Skill: Calculate the surface area of prisms

Surface area is the total area covering every outside face of a prism. It includes:

• two congruent bases
• all the lateral faces connecting the bases

For a prism, use

$$SA=2B+Ph$$

where:

• $B$ is the area of one base
• $P$ is the perimeter of one base
• $h$ is the length of the prism

The answer is written in square units because we are finding area, not volume.

Example: Find the surface area of a rectangular prism with a base that is $3$ units by $4$ units and a prism length of $10$ units.

Step 1: Find the area of one base.

The base is a rectangle:

$$B=3\cdot4=12\text{ square units}$$

Step 2: Find the perimeter of the base.

$$P=3+4+3+4=14\text{ units}$$

Step 3: Substitute into the formula.

$$SA=2B+Ph$$ $$SA=2(12)+14(10)$$

Step 4: Calculate.

$$SA=24+140=164$$

The surface area of the prism is

$$\boxed{164\text{ square units}}$$

The $24$ represents the two bases, and the $140$ represents the total area of the four lateral faces.