Question

How do you calculate the surface area of a regular prism that is $400$ by $600$ by $800$?

Answer 1

Hint: This is the question on the topic of mensuration. We do know the three sides of the prism, since the three sides are different and they make a prism it can be inferred as a rectangular prism. The formula for the surface area of the prism is $l\times b\times h$ , where all three are the dimensions of the prism.

Complete step-by-step solution:
To make calculation a bit easier we will draw a prism. Here $lh$ is the area of side with one side as $l$ and another as $h$, $lb$ is the area of side with one side as $b$ and another as $l$ and $bh$ is the area of side with one side as $b$ and another as $h$. On folding it forms a figure called the right rectangular prism.

According to the question given, let us consider $l=600$, $b=400$ and $h=800$. So the surface area of the rectangular prism will be $lb+bh+lh+lb+bh+lh$. On putting the values in the formula equation.
$lb+bh+lh+lb+bh+lh = 2lb+2lh+2bh$
$2\Rightarrow 600\times 400+2\times 400\times 800+2\times 600\times 800$
On multiplying each number
$\Rightarrow 480000+640000+960000$
Adding all the terms we get
$\Rightarrow 2080000$
$\therefore $ The surface area of the given prism having sides 400 , 600 and 800 is $2080000$.

Note: To solve questions like this we need to keep in mind the formulas for the figures or you can say shapes.
Do remember while calculating the surface area if we analyse the figure and then solve, its calculation becomes easier. Calculate the area part wise to find the surface area of the whole figure. This makes the calculation much easier. Drawing the figure will make calculation convenient.