Question Number 9168 by nazar last updated on 21/Nov/16
$$\mathrm{If}\:\mathrm{all}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{hexagon}\:\mathrm{is}\:\mathrm{increased} \\ $$$$\mathrm{by}\:\mathrm{2\%}.\:\mathrm{Find}\:\mathrm{the}\:\%\:\mathrm{increase}\:\mathrm{in}\:\mathrm{its}\:\mathrm{area}. \\ $$
Answered by mrW last updated on 22/Nov/16
$$\mathrm{1}.\mathrm{02}^{\mathrm{2}} =\mathrm{1}.\mathrm{0404}=\mathrm{104}.\mathrm{04\%} \\ $$$$\mathrm{i}.\mathrm{e}.\:\mathrm{its}\:\mathrm{area}\:\mathrm{increases}\:\mathrm{by}\:\mathrm{4}.\mathrm{04\%}. \\ $$$$ \\ $$
Commented by RasheedSoomro last updated on 22/Nov/16
$$\boldsymbol{\mathrm{Area}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{hexagon}}\:\mathrm{not}\:\mathrm{area}\:\mathrm{of}\:\mathrm{square}! \\ $$
Commented by mrW last updated on 22/Nov/16
$$\mathrm{it}'\mathrm{s}\:\mathrm{valid}\:\mathrm{for}\:\mathrm{arbitrary}\:\mathrm{n}−\mathrm{polygon}. \\ $$
Commented by mrW last updated on 22/Nov/16
$$\mathrm{The}\:\mathrm{increase}\:\left(\mathrm{or}\:\mathrm{decrease}\right)\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{is}\:\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{square} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{increase}\:\left(\mathrm{or}\:\mathrm{decrease}\right)\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{perimeter}. \\ $$