Question

Find the surface area of rectangular prism where the area of each small square is $=1{{m}^{2}}$

(a). $180{{m}^{2}}$
(b). $202{{m}^{2}}$
(c). $313{{m}^{2}}$
(d). $188{{m}^{2}}$

Answer 1

- Hint: First, we have to find the length, width and height of the prism by looking at the diagram as values are not given directly in question. Further, we have to use formula of surface area of prism which is $2\left[ \left( \text{length}\times \text{breadth} \right)+\left( \text{breadth}\times \text{height} \right)+\left( \text{length}\times \text{height} \right) \right]$ .

Complete step-by-step solution -

Here, we need to understand what a rectangular prism is.
A rectangular prism is a six-faced 3-D solid in which all the faces are rectangles. All these faces meet at right angles to one another. For example: matchbox is the simple object to understand rectangular prisms.
Now, by looking at the diagram given in the question, we need to identify length(l), breadth(b) and height(h).
 

Now, to find the value of length, breadth and height we need to count the square box along its sides.
Along the base side, which is length we can count that there are 7 square boxes. So, length $l=7m$ ,
Similarly, Breadth $b=4m$ and height $h=6m$ .
Now, applying the formula of surface area of prism which is: $2\left[ \left( \text{length}\times \text{breadth} \right)+\left( \text{breadth}\times \text{height} \right)+\left( \text{length}\times \text{height} \right) \right]$
Therefore, substituting all the values in this equation, we get
Surface area $=2\left[ \left( 7\times 4 \right)+\left( 4\times 6 \right)+\left( 7\times 6 \right) \right]$
$=2\left[ 28+24+42 \right]$
$=2\times 94$
$=188{{m}^{2}}$
Thus, the surface area of the rectangular prism is $188{{m}^{2}}$ .
Hence, option (d) is the correct answer.

Note: Students generally get confused between the surface area of cuboid and rectangular prism. Formula for these both are slightly different i.e. for cuboid, it is $\left[ \left( \text{length}\times \text{breadth} \right)+\left( \text{breadth}\times \text{height} \right)+\left( \text{length}\times \text{height} \right) \right]$ and for rectangular prism as it consist of 6 faces is it just multiplied by number 2 $\times $ surface area of cuboid. Also, don’t understand that as per diagram in question prism is decorated by squares in it but they are used to find dimensions like length, breadth and height.