The formula for the lateral area of a rectangular prism is:

$S$lateral​=C×h

Where,

Slateral​ represents the lateral area of the rectangular prism,

$C$ represents the perimeter of the base of the rectangular prism,

$h$ represents the height of the rectangular prism.

This formula is based on the geometric characteristics of the rectangular prism, specifically, its lateral surfaces are composed of rectangles determined by the perimeter of the base and the height. Therefore, the lateral area can be calculated by multiplying the perimeter of the base with the height.

A common example of a rectangular prism item is a cardboard box with a rectangular base. Let’s assume we have a cardboard box with a rectangular base that measures 10 cm in length and 5 cm in width, and a height of 8 cm.

First, we need to calculate the perimeter of the base, $C$. For a rectangle, the perimeter $C$ is twice the sum of the length and width:
$C=2\times (10\text{ cm}+5\text{ cm})=2\times 15\text{ cm}=30\text{ cm}$

Next, we will substitute the base perimeter $C$ and the height $h$ into the formula for the lateral area of a rectangular prism, Slateral​=C×h, to calculate the result:
Slateral​=30 cm×8 cm=240 cm².

Therefore, the lateral area of this rectangular cardboard box is $240\text{ cm²}$.

Please note that this calculation only considers the lateral area of the box and does not include the areas of the base and top. If you need to calculate the total surface area of the box, you would also need to add the areas of the base and top.

Recommended readings: “Formula for the Lateral Area of a Regular Pyramid,” “Formula for the Lateral Area of a Pyramid,” “Formula for the Lateral Area of a Rectangular Prism,” “Formula for the Lateral Area of a Regular Prismoid.”