πR²-πr²=36π
R²-r²=36
(R-r)(R+r)=36 (1)
inaltimea in triunghiul echilateral h= R+r
adica R=2h/3
r=h/3
inlocuim in (1)
(2h/3-h/3)(2h/3+h/3)=36
h/3 ×h=36
h²=108
h=6√3
inaltimea in functie de latura triunghiului echilateral h=L√3/2
deci L=2*h/√3=2*6√3/√3=12
Atriunghi=12×6√3/2=36√3
