On a rectangular plot of length 7 meters and breadth 6 meters, a square side 3 meters is made. Find the area of the remaining plot.

Hint: In this question first find the area of the rectangular plot and also fins the area of the square and then subtract the total area of the plot with the square side to find the remaining plot. For this, we will calculate the area of the full plot and then subtract the area of the square side to find the area of the remaining plot. The area of a rectangle is given by the formula \[Area = l \times b\] , where \[l\] is the length of the rectangle and \[b\] is the breadth of the rectangle

Complete step-by-step answer:

The length of the rectangular plot \[l = 7\;m\] .
The breadth of the rectangular plot \[b = 6\;m\] .
We know the area of a rectangle is given by the formula \[Area = l \times b\] , so the area of the rectangular plot of length 7 m and breadth 6 m will be
 \[
\Rightarrow Area = l \times b \\
   = 7 \times 6 \\
   = 42\;{m^2} \;
 \]
Also given the length of square side 3 m, so the area of the side of the square which is given by the formula \[Area = {a^2}\] , will be
 \[
\Rightarrow Area = {3^2} \\
   = 9\;{m^2} \;
 \]
From the given figure we need to find the area of the un-shaded area by subtracting the area of the rectangular plot by the area of the shaded portion which is the square side.
Hence, we can write,
Area of the remaining plot \[ = 42 - 9 = 33\;{m^2}\]
Therefore, the required area is \[ = 33\;{m^2}\]
So, the correct answer is “\[ = 33\;{m^2}\] ”.

Note: It is interesting to note here that in this question, a small rectangular section has been cut out from the big rectangular plot and so the total area of the rectangular plot will certainly decrease. The area of the rectangular plot is given by the formula \[Area = l \times b\] , where \[l\] is the length and $b$ is the width of the rectangle.