Find surface area of rectangular prisms

Surface area is the total area of the six rectangular faces of a rectangular prism, found by interpreting a net or combining the areas of three pairs of congruent faces: $2(lw+lh+wh)$ , expressed in square units. The dimensions must use consistent units, and surface area must be distinguished from volume, which measures space inside; more general three-dimensional solids and advanced algebraic generalizations are not included.

Detailed Explanation: 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.

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Surface Area of a Rectangular Prism - Count Blocks

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