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Source : calculaire.mp

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calculaire.mp
prologues:=2;
input geometriesyr16;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
u:=7.5mm;
pair A,B,C,D,E,F,G,H;
A=u*(2,7);
B=A shifted(u*(0,3));
C=B shifted(u*(8,0));
E=C shifted(u*(0,-6));
H-B=E-C;
path cc;
cc=cercledia(C,E);
D=point(0.55*length cc) of cc;
F=E shifted(u*(-6,0));
G=(xpart(F),ypart(A));
trace A--B--C--D--E--F--G--cycle;
trace C--E dashed evenly;
trace cotationmil(B,C,2mm,20,btex 20~cm etex);
trace cotation(A,B,-5mm,-2mm,btex 5~cm etex);
trace cotationmil(E,C,-5mm,20,btex 10~cm etex);
trace cotation(D,C,-4mm,-2mm,btex 8~cm etex);
trace cotation(D,E,-2mm,-2mm,btex 6~cm etex);
nomme.llft(A);
nomme.ulft(B);
nomme.urt(C);
nomme.lft(D);
nomme.lrt(E);
nomme.llft(F);
nomme.urt(G);
trace codesegments(G,A,A,B,1);
drawoptions(withpen pencircle scaled 1.25bp);
trace codeperp(A,B,C,5);
trace codeperp(B,C,E,5);
trace codeperp(C,D,E,5);
trace codeperp(E,F,G,5);
trace codeperp(F,G,A,5);
trace codeperp(G,A,B,5);
picture fond;
fond=currentpicture;
drawoptions();
pair U,W,X,Y,Z;
U=iso(A,B,C,D,E,F,G);
W=u*(2,2);
X-W=u*(4.5,0);
Y-X=u*(3.5,0);
Z-Y=u*(2.5,0);
fin;
_nfig:=0;
for k=0 upto 2:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  fin;
endfor;
vues=2;
fillcolor:=jaune;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  fin;
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  transparence (H--B--C--E--cycle);
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  fin;
endfor;
fillcolor:=bleu;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  fin;
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  transparence H--A--G--F--cycle;
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  fin;
endfor;
fillcolor:=orange;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  fin;
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  transparence C--D--E--cycle;
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  remplis ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z withcolor orange;
  trace ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z;
  trace chemin(3.5/10[Y,Z],5.5/10[Y,Z]) withpen pensquare scaled2bp;
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  remplis ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z withcolor orange;
  trace ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z;
  trace chemin(3.5/10[Y,Z],5.5/10[Y,Z]) withpen pensquare scaled2bp;
  label(btex $\cal S$ etex,W+u*(0,-1.5));
  label(btex $=$ etex,1/2[X,W]+u*(0,-1.5));
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  remplis ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z withcolor orange;
  trace ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z;
  trace chemin(3.5/10[Y,Z],5.5/10[Y,Z]) withpen pensquare scaled2bp;
  label(btex $\cal S$ etex,W+u*(0,-1.5));
  label(btex $=$ etex,1/2[X,W]+u*(0,-1.5));
  label(btex $20\times10$ etex,X+u*(0,-1.5));
  label(btex $-$ etex,0.65[X,Y]+u*(0,-1.5));
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  remplis ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z withcolor orange;
  trace ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z;
  trace chemin(3.5/10[Y,Z],5.5/10[Y,Z]) withpen pensquare scaled2bp;
  label(btex $\cal S$ etex,W+u*(0,-1.5));
  label(btex $=$ etex,1/2[X,W]+u*(0,-1.5));
  label(btex $20\times10$ etex,X+u*(0,-1.5));
  label(btex $-$ etex,0.65[X,Y]+u*(0,-1.5));
  label(btex $5\times5$ etex,Y+u*(0,-1.5));
  label(btex $-$ etex,0.45[Y,Z]+u*(0,-1.5));
  fin;
endfor;
for k=0 upto vues:
  u:=1cm;
  figure(0,0,11u,8u);
  u:=7.5mm;
  trace fond;
  trace ((A--B--C--D--E--F--G--cycle) shifted(-U)) xscaled0.4 yscaled0.4 shifted W;
  trace chemin(2/5[W,X]+u*(0,0.25),3/5[W,X]+u*(0,0.25)) withpen pensquare scaled2bp;
  trace chemin(2/5[W,X]+u*(0,-0.25),3/5[W,X]+u*(0,-0.25)) withpen pensquare scaled2bp;
  remplis ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X withcolor jaune;
  trace ((H--B--C--E--cycle) shifted(-iso(H,B,C,E))) xscaled0.4 yscaled0.4 shifted X;
  trace chemin(5.5/10[X,Y],7.5/10[X,Y]) withpen pensquare scaled2bp;
  remplis ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y withcolor bleu;
  trace ((H--A--G--F--cycle) shifted(-iso(H,A,G,F))) xscaled0.4 yscaled0.4 shifted Y;
  remplis ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z withcolor orange;
  trace ((C--D--E--cycle) shifted(-iso(C,D,E))) xscaled0.4 yscaled0.4 shifted Z;
  trace chemin(3.5/10[Y,Z],5.5/10[Y,Z]) withpen pensquare scaled2bp;
  label(btex $\cal S$ etex,W+u*(0,-1.5));
  label(btex $=$ etex,1/2[X,W]+u*(0,-1.5));
  label(btex $20\times10$ etex,X+u*(0,-1.5));
  label(btex $-$ etex,0.65[X,Y]+u*(0,-1.5));
  label(btex $5\times5$ etex,Y+u*(0,-1.5));
  label(btex $-$ etex,0.45[Y,Z]+u*(0,-1.5));
  label(btex $(8\times6)\div2$ etex,Z+u*(0,-1.5));
  fin;
endfor;
end