Question 1179702

let the side of square be {{{a}}}

the area {{{A=a^2}}}


since <{{{ ABC}}} (interior angle of the octagon) is {{{135}}}°, we can use cosine formula to calculate {{{a}}}


{{{a^2=2^2+2^2-2*2*2*cos(135)}}}


{{{a^2=8-8*cos(135)}}}....write {{{cos(135)}}} as a {{{cos(180-45)=cos(-45)=-cos(45)}}}


{{{a^2=8-8*(-cos(45))}}}............{{{-cos(45)=-sqrt(2)/2}}}


{{{a^2=8-8*(-sqrt(2)/2)}}}


{{{a^2=8+4sqrt(2)}}}


{{{a^2=13.7}}}


=> the area {{{A=13.7cm^2}}}