Question 1175874


here you have equaterial triangle and side length is equal to the  diagonal of a cube

if a cube of side length {{{2cm}}}, diagonal is

{{{d=sqrt((2cm)^2+(2cm)^2)}}}
{{{d=sqrt(4cm^2+4cm^2)}}}
{{{d=sqrt(2*4)cm}}}
{{{d=2sqrt(2)cm}}}

=> equal to the side {{{a}}} of a equaterial  triangle

{{{a=2sqrt(2)cm}}}

we need height of a triangle

{{{h=sqrt(a^2-(a/2)^2)}}}

{{{h=sqrt((2sqrt(2))^2-(2sqrt(2)/2)^2)}}}

{{{h=sqrt(8-(8/4))}}}
{{{h=sqrt(8-2)}}}
{{{h=sqrt(6)}}}

 the area of the triangle:

{{{A=ah/2}}}

{{{A=(sqrt(8)*sqrt(6))/2}}}
{{{A=2 sqrt(3)cm^2}}}->exact solution
{{{A=3.46cm^2}}}