Task 641
Task 641: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Given that $BDEF$ is a square and $AB = BC = 1$, find the number of square units in the area of the regular octagon. asy real x = sqrt(2); pair A,B,C,D,E,F,G,H; F=(0,0); E=(2,0); D=(2+x,x)…
The task
Given that $BDEF$ is a square and $AB = BC = 1$, find the number of square units in the area of the regular octagon. [asy] real x = sqrt(2); pair A,B,C,D,E,F,G,H; F=(0,0); E=(2,0); D=(2+x,x); C=(2+x,2+x); B=(2,2+2x); A=(0,2+2x); H=(-x,2+x); G=(-x,x); draw(A--B--C--D--E--F--G--H--cycle); draw((-x,0)--(2+x,0)--(2+x,2+2x)--(-x,2+2x)--cycle); label("$B$",(-x,2+2x),NW); label("$D$",(2+x,2+2x),NE); label("$E$",(2+x,0),SE); label("$F$",(-x,0),SW); label("$A$",(-x,x+2),W); label("$C$",(0,2+2x),N); [/asy]