Question

The central hall of a school is $18m$ long and $12.5m$ wide. A carpet is to be laid on the floor leaving a strip $50cm$ wide near the walls, uncovered. Find the area of the carpet and also the uncovered portion?

• A. $195.5m^2$.
• B. $105.5m^2$.
• C. $155.5m^2$.
• D. None of these

Answer 1

The correct option is A $195.5m^2$.

Length of hall $SR=\left(l\right)=18m$

Breadth of hall $RQ=\left(b\right)=12.5m$

$\therefore$ Area of hall $=l\times b=18\times 12.5=225m^2$

strip $=50cm=0.5m$

Now, Length of carpet $CD=(18-0.5-0.5)=17m[\because 1m=100cm\Rightarrow 50cm=0.5m]$

and, Breadth of carpet $BC=(12.5-0.5-0.5)=11.5m$

$\therefore$ Area of carpet $=CD\times BC=17\times 11.5=195.5m^2$

Now, Area of uncovered region $=$ Area of hall $-$ Area of carpet $=225-195.5=29.5m^2$

So, $\text{A}$ is the correct option.