Question

How do you find the area of the lateral side?

Answer 1

This problem deals with finding the lateral surface area of the rectangular prism. The lateral surface area of any right rectangular prism is equivalent to the perimeter of the base times of the height of the prism. Therefore, the lateral surface area of a rectangular prism is given by the formula:
$\Rightarrow 2\left( {l + w} \right)h$ square units
Where $l$ is the length, $w$ is the width and $h$ is the height of the rectangular prism.

Complete step-by-step answer:
Here given that the height is given by:
$\Rightarrow h = 6$
The width is given by:
$\Rightarrow w = 3$
The length is given by:
$\Rightarrow l = 2$
So the perimeter is given by $p$:
$\Rightarrow p = 2\left( {l + w} \right)$
$\Rightarrow p = 2\left( {2 + 3} \right)$
So the perimeter of the rectangular prism is :
$\therefore p = 10$
So this is the perimeter of the base, which is the grayed-in region as given in the picture.
We know that the perimeter of any shape is just the sum of all the sides added together.
Now finding the lateral surface area of the rectangular prism by applying the given formula, as shown below:
$\Rightarrow 2\left( {l + w} \right)h$
On substituting the values of the expressions obtained, as shown below:
$\Rightarrow 10 \times 6$
$\Rightarrow 60$ square cm.
$\therefore$The area of the lateral side or the lateral surface area is equal to 60 sq.cm

Final answer: The area of the lateral side is 60 sq.cm.

Note:
Please note that the lateral indicates the side of something. Therefore the lateral surface area is found by finding the surface area of the sides of the object. This is done by finding the perimeter of the base and multiplying it by the height of any three-dimensional figure.