Problema di trigonometria/geometria analitica

Vertici esterni
* A(- 5, - 5), B(+ 5, - 5), C(+ 5, + 5), D(- 5, + 5)
Rette
* BE ≡ y = - 5 + (x - 5)*tg(- π/3) ≡ y = 5*(√3 - 1) - (√3)*x
* DH ≡ y = + 5 + (x + 5)*tg(- π/6) ≡ y = 5*(3 - √3)/3 - x/√3
Intersezioni
* BE & asse x ≡ (y = 5*(√3 - 1) - (√3)*x) & (y = 0) ≡ J(5*(3 - √3)/3, 0)
* BE & DH ≡ (y = 5*(√3 - 1) - (√3)*x) & (y = 5*(3 - √3)/3 - x/√3) ≡ N(5*(2 - √3), 5*(2 - √3))
* asse y & DH ≡ (x = 0) & (y = 5*(3 - √3)/3 - x/√3) ≡ I(0, 5*(3 - √3)/3)
Distanze (L)
* |OI| = |OJ| = 5*(3 - √3)/3
* |NI| = |NJ| = 10*√((7 - 4*√3)/3) ~= 1.54701 (lato L dell'ottagono)
Area (S)
* S(ONJ) = b*h/2 = (xJ)*(yN)/2 = (xJ)*(yN)/2 =
= (5*(3 - √3)/3)*(5*(2 - √3))/2 = 25*(9 - 5*√3)/6
POLIGONO P
* perimetro p = 8*L = 80*√((7 - 4*√3)/3) ~= 12.376 cm
* asea S(P) = 8*S(ONJ) = 100*(9 - 5*√3)/3 ~= 11.3249 cm^2