Question 693724
given:
side length {{{a=10m}}}

{{{drawing( 600,600, -5, 10, -5, 10, 
         grid(0),locate( 4, 4, H ),locate( 8, 4, E ),locate( 8, 8, F ),locate( 4, 8, G ),locate( 1, 1, A ),locate(6, 1, B),locate( 6, 6, C ),locate( 1, 6, D ),line(1, 1, 6, 1 ),line(1, 1, 1, 6 ),line(6, 1, 6, 6 ),line(1, 6, 6, 6 ),line(1, 6, 4, 8 ),line(6, 1, 8, 4 ),line(8, 8, 4, 8 ),line(6, 6, 8, 8 ),line(8, 8, 8, 4 ),line(8, 8, 1, 1 ),line(1, 1, 8, 4),line(4, 8, 4, 4),line(8, 4, 4, 4),line(1, 1, 4, 4),locate( 3, 0.8, a=10m ),locate( 7, 1.8, a=10m ),locate( 4, 3, d[1] ),locate( 5.2, 5, d )
)}}}

use Pythagorean theorem to find first the length of shorter diagonal {{{AE=d[1]}}}:

{{{d[1]^2=a^2+a^2}}}

{{{d[1]^2=10^2+10^2}}}

{{{d[1]^2=100+100}}}

{{{d[1]^2=200}}}

{{{d[1]=sqrt(200)}}}

{{{highlight(d[1]=14.14)}}}

now we can find longer diagonal ({{{AF=d}}}) as a hypotenuse of a right-angle triangle {{{AEF}}}

{{{d^2=d[1]^2+a^2}}}

{{{d^2=(14.14)^2+10^2}}}

{{{d^2=200+100}}}

{{{d^2=300}}}

{{{d=sqrt(300)}}}

{{{highlight(d=17.32)}}}