Constructing a square with area 5

five-times-square.eukleides

let(
middle, point(3/2,3/2),
t, point(0,1)..point(2,1)..point(2,0),
t2, point(0,1)..point(2,0)..point(0,0),
colors, qualitative_color_schemes(5)[0],

eukleides("A 3×3 grid of squares. The middle square is filled in, and the 2×1 rectangles around it each have half filled in. The filled-in shapes together make a square whose corners touch the edges of the grid.",
[
  map(x filled color, [x,color], zip(iterate(rotate(tri,middle,deg(90)),tri,t,3), colors))
, map(x filled color opacity(0.3), [x,color], zip(iterate(rotate(tri,middle,deg(90)),tri,t2,3), colors))
, polygon(iterate(rotate(p,middle,deg(90)), p, point(0,1), 4)) dashed
, polygon(square(point(1,1),1)) filled colors[4]

, ( map(point(x,0)..point(x,3), x, 0..3)
  + map(point(0,y)..point(3,y), y, 0..3)
  ) white
]
)

)