[attach]3170[/attach] [attach]3171[/attach] [attach]3172[/attach] [attach]3173[/attach]

[attach]121886[/attach] angolo ABC = π(1-1/3-1/5 = 7π/15 cos (7π/15) = 0,1045 AC = √( (8√3)^2+20^2-2*20*(8√3)*0,1045) = 64*3+400-320√3*0,1045 = 23,1 semiperimetro p = 8√3+20+23,1 = 56,96 cm area = √(28,48*(28,48-8√3)*(28,48-20)*(28,48-23,1)) = 137,8 (arrotond. a 138)

Es. 150. $8sin alpha è l'altezza del triangolo, quindi $17*8sin alpha /2=60$ Pertanto sin alpha =15/17$ e quindi alpha =arcsin(15/17)$

[attach]121883[/attach] area ABC = 60 = AB*CH/2 area ABC = 17*8*sin α /2 60 = 17*4*sin α sin α = 15/17 angolo α = arcsin 15/17

[attach]121885[/attach] EB = EC = 2√2 BC = √8+8-2*8*0,866 = 1,464 angolo DEC = 105-(180-30)/2 = 30° ED = 8+9-2*6√2*0,8668+9-2*6√2*0,866 = 2,30 altezza EH = √8-(1,464/2)^0,5 = 2,673 area ABE = 2^2/2 = 2,0 cm^2 area BCE = b*h/2 = 1,464*2,673/2 = 1,96 cm^2 semiperimetro EDC = (2√2+3+2,30)/2 = 4,066 area EDC = √4,066*(4,066-2,82)*(4,066-3)*(4,066-2,30) = 3,09 cm^2 area totale = 2+1,96+3,09 = 7,045 cm^2