Calculate the surface area of rectangular prisms

Surface area of a rectangular prism is the total area of its six rectangular faces, found by recognizing three pairs of congruent faces and calculating $2lw+2lh+2wh$ , or by decomposing a net into rectangles. Dimensions may be given as whole numbers, decimals, or common fractions, and the result is expressed in square units; this understanding distinguishes surface area from volume and does not extend to curved or composite solids.

Detailed Explanation: Calculate the surface area of rectangular prisms

A rectangular prism has six rectangular faces. Each pair of opposite faces is the same size, so you can find the total area with

SA=2lw+2lh+2wh

where:

$l$ is the length,
$w$ is the width,
$h$ is the height,
$(SA)$ is the surface area.

Example

Find the surface area of a rectangular prism with length $8$ cm, width $3$ cm, and height $5$ cm.

Step 1: Identify the dimensions.

l=8\text{ cm},\qquad w=3\text{ cm},\qquad h=5\text{ cm}

Step 2: Substitute into the formula.

SA=2(8)(3)+2(8)(5)+2(3)(5)

Step 3: Find the area of each pair of faces.

2(8)(3)=48

2(8)(5)=80

2(3)(5)=30

Step 4: Add the areas.

SA=48+80+30=158

Answer:

\boxed{158\text{ cm}^2}

Surface area is measured in square units because it measures the area covering the outside of the prism. It is different from volume, which measures the space inside and uses cubic units.

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Surface Area of a Rectangular Prism - Count Blocks

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