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: First of all, find the area of the floor by using the formula for area of rectangle. Now, find the area of square carpet that is to be laid. Thus, subtract the area of carpet from the area of the floor.

Complete step-by-step answer:

Firstly, we may calculate the area of the floor in which carpet is to be laid.
For calculating the area of the floor, we will use the formula for area of rectangle \[A = l \times b\] .
 \[
  l = 5m \\
  b = 4m \\
 \]
Now, area of floor
 \[
  {A_f} = 5m \times 4m \\
  \therefore {A_f} = 20{m^2} \\
 \]
Then, we have to find the area of a square carpet which is to be laid \[A = {l^2}\] .
 \[l = 3m\]
Now, area of carpet
 \[{A_c} = {\left( {3m} \right)^2}\]
 \[\therefore {A_c} = 9{m^2}\]
For calculating the area left, we have to subtract area of carpet from area of floor i.e. \[{A_l} = {A_f} - {A_c}\] .
 \[
  \therefore {A_l} = 20{m^2} - 9{m^2} \\
  \therefore {A_l} = 11{m^2} \\
 \]
Thus, the 11 square meters area of the floor remains non-carpeted.

Note: Always remember to subtract bigger value from smaller value. Remember the basic formula of area so that it will help us in easy calculation.