Question

A floor is 5m long and 4m wide. A square carpet of sides 3m is laid on the floor. Find the area of the floor that is not carpeted.

Answer 1

Hint: In this question read the given information to identify the given dimensions also remember that to use the formula of area of rectangle i.e. $area = length \times breadth$ and the area of square i.e. $area = {\left( {side} \right)^2}$, use this information to approach the solution.

Complete step-by-step answer:
According to the given information we have a floor which is 5 m long and 4m wide so we can say that the shape of floor is in rectangle also it is given that carpet of square shape of side 3m
So, the given dimensions are length of the floor is 5m, breadth of the floor is 4m
Now using the formula of area of rectangle i.e. $area = length \times breadth$ to find the area of the floor
Substituting the values in the above formula we get
Area of floor = $5m \times 4m = 20{m^2}$
Now let’s find the area of carpet using the formula of area of square i.e. $area = {\left( {side} \right)^2}$
It is also given that side of the carpet is 3m
Now substituting the values in the above formula, we get
Area of carpet = $3m \times 3m = 9{m^2}$
To find the area of the floor that is not carpeted,
We will subtract the area of the floor from area of carpet
Now area which is not carpeted = $20{m^2} - 9{m^2} = 11{m^2}$
Therefore, the area of floor that is not covered by carpet is equal to $11{m^2}$

Note: This is the question of mensuration, in order to find the area of not covered area by carpet one should first proceed to identify the shape of floor using the given dimensions and then he can find the area of floor of rectangular shape and carpet of square shape separately and then can subtract the area of the floor from the area of carpet which will result in area of non-covered floor by carpet.