Question

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

Answer 1

The area $A$ of the rectangle with length $l$ and width $w$ is given by, $A=l\times w$.

The area $A$ of the square with side $s$ is given by, $A=s\times s$.

Step 1: Substitute $l=5$, $w=4$ into the formula $A=l\times w$ and find the area of the floor.

$\begin{array}{rcl}A& =& 5\times 4\\ & =& 20{\text{m}}^2\end{array}$

Step 2: Substitute $s=3$ into the formula $A=s\times s$ and find the area of the square carpet.

$\begin{array}{rcl}A& =& 3\times 3\\ & =& 9{\text{m}}^2\end{array}$

Step 3: Subtract the area of carpet from the area of the floor to find the area of the floor that is not carpeted.

$20-9=11{\text{m}}^2$

Hence, the area of the floor that is not carpeted is $11{\text{m}}^2$.