Examples - geometric figures

• Circle, Kite, Parallelogram, Rectangle, Regular Polygon, Rhombus, Square, Trapezoid, Triangle

R=6; /* radius */
s=deg30; /* central angle */
print "Circle
 circle area=",pi*R^2,"
 circumference=",2*pi*R,"
 sector area=",torad(s)*R^2/2,"
 arc length=",torad(s)*R,"
 chord length=",2*R*sin(s/2),"
 segment area=",(torad(s)-sin(s))*R^2/2,"
 segment height=",R*(1-cos(s/2))

c=4.4721; d=2.8284;   /* sides */
f=4; g=6;   /* diagonals */
print "Kite
 area=",(f*g)/2,"
 perimeter=",2*(c+d)

L=4.5; /* lateral side */
W=6;  /* base side */
h=4;  /* height */
print "Parallelogram
 area=",W*h,"
 perimeter=",2*(L+W),"
 diagonal p=",sqrt(W^2+L^2+2*W*sqrt(L^2-h^2)),"
 diagonal q=",sqrt(W^2+L^2-2*W*sqrt(L^2-h^2)),"
 alpha=",asin(h/L),"
 beta=",deg180-Ans

L=6; W=5;
print "Rectangle
 area=",L*W,"
 perimeter=",2*(L+W),"
 diagonal=",hypot(L,W)

n=5; /* number of vertices */
s=6; /* side length */
print "Regular polygon
 area=",s^2*n/4*cot(deg180/n),"
 perimeter=",s*n,"
 angle=",(1-2/n)*deg180,"
 circumradius=",s/2/sin(deg180/n),"
 apothem=",s/2*cot(deg180/n)

s=5; h=4.5;
print "Rhombus
 area=",s*h,"
 perimeter=",4*s,"
 diagonal p=",sqrt(2*s*(s+sqrt(s^2-h^2))),"
 diagonal q=",sqrt(2*s*(s-sqrt(s^2-h^2))),"
 alpha=",asin(h/s),"
 beta=",deg180-Ans

s=6;
print "Square
 area=",s^2,"
 perimeter=",4*s,"
 diagonal=",s*sqrt2

a=6; b=3; /* parallel bases */
c=3; d=3.5; /* lateral sides */
print "Trapezoid
 height=",h=sqrt((-a+b+c+d)*(a-b+c+d)*(a-b+c-d)*(a-b-c+d))/2/abs(b-a),"
 area=",(a+b)/2*h,"
 perimeter=",a+b+c+d,"
 alpha=",asin(h/c),"
 beta=",asin(h/d)

a=3; b=4; c=5;
p=(a+b+c)/2; S=sqrt(p*(p-a)*(p-b)*(p-c));
if(real ans,gotor3,0);
print"Triangle inequality is false !";return;
print"Triangle
alpha=",acos((b^2+c^2-a^2)/(2*b*c)),"
beta=",acos((a^2+c^2-b^2)/(2*a*c)),"
gamma=",acos((b^2+a^2-c^2)/(2*b*a)),"
Perimeter=",a+b+c,"
Area=",S,"
Incircle=",S/p,"
Circumscribed circle=",a*b*c/4/S,"
Altitude a=",2*S/a,"
Altitude b=",2*S/b,"
Altitude c=",2*S/c,"
Median a=",sqrt(2*(b^2+c^2)-a^2)/2,"
Median b=",sqrt(2*(a^2+c^2)-b^2)/2,"
Median c=",sqrt(2*(b^2+a^2)-c^2)/2