Question

a path of uniform width 3m runs inside a hall which is 24 m long and 18m broad find the area of the path and cost of flooring it at the rate of rupees 5 per square metre.

Answer 1

area of the path is 216m^2

Answer 2

Therefore Area of path $216 m^{2}$

And cost of flooring is $1080$ rupees

Step-by-step explanation:

Given;

$24$ m long and $18$ m broad of a Hall and a path of uniform width $3$m

From figure;

For hall $AB=DC=18$m, $AD=BC=24$m and

$ab=cd=12$m, $ad=bc=18$

 Area of Hall $(ABCD)=AB\times BC$

⇒Area of Hall $(ABCD)=24\times 18$

∴Area of Hall $(ABCD)=432$ $m^{2}$

And,

Area of $abcd=ab\times bc$

⇒Area of $abcd=18\times 12$

∴ Area of $abcd=216$ $m^{2}$

∴ Area of path$=$ Area of $ABCD-$ Area of $abcd$

⇒Area of path$=$ $432-216$

∴Area of path $=216 m^{2}$

And cost of flooring$=216\times 5=1080$ rupees