2. `h = "15 cm"`

`"I. rombusz"`
`e = "18 cm, "f = "15 cm"`

`T_a = (e*f)/2 = (18*15)/2 = 9*15 = "135 cm"^2`

`a = sqrt((e/2)^2+(f/2)^2) = sqrt(9^2+(15/2)^2) = sqrt(549/4) = (3 sqrt 61)/2 ~~ "11,715 cm"`

Kétféle oldaléle lesz:
`b_1 = sqrt((f/2)^2+h^2) = sqrt((15/2)^2+15^2) = sqrt("1 125"/4) = (15 sqrt 5)/2 ~~ "16,771 cm"`

`b_2 = sqrt((e/2)^2+h^2) = sqrt(9^2+15^2) = sqrt(306) = 3 sqrt 34 ~~ "17,493 cm"`

Viszont csak egyféle oldallap terület:
`s = (a+b_1+b_2)/2 = ((3 sqrt 61)/2+(15 sqrt 5)/2+3 sqrt 34)/2 ~~ "22,989 cm"`

`T_o = sqrt(s(s-a)(s-b_1)(s-b_2)) = (45 sqrt(70))/4 ~~ "94,124 cm"^2`

a) `V = (T_a*h)/3 = (135*15)/3 = "675 cm"^3`

b) `F = T_a+P = T_a+4 T_o = 135+4*(45 sqrt(70))/4 = 135+45 sqrt(70) ~~ "511,497 cm"^2`

`"II. szabályos ötszög"`
`a = "9 cm"`

Az alap 5 háromszögre bontható. Ezek magassága:
`"tg"((180°)/5) = (a/2)/m => m = a/(2\ "tg"\ 36°) = a/2\ "ctg"\ 36° = 9/2\ "ctg"\ 36° ~~ "6,194 cm"`

`T_a = 5*((a*m)/2) = 5*(a^2/2\ "ctg"\ 36°)/2 = 5/4 a^2\ "ctg"\ 36° = 5/4*9^2\ "ctg"\ 36° ~~ "139,359 cm"^2`

Az oldallapok magassága:
`m_o = sqrt(h^2+m^2) = sqrt(15^2+9^2/4\ "ctg"^2\ 36°) = sqrt(15^2+9^2/4 (1+2/sqrt(5))) ~~ "16,228 cm"`

`P = 5 T_o = 5*((a*m_o)/2) = (5*9)/2*m_o ~~ "365,140 cm"^2`

a) `V = (T_a*h)/3 = (5/4*9^2\ "ctg"\ 36°*15)/3 = (5^2*9^2)/4\ "ctg"\ 36° ~~ "696,793 cm"^3`

b) `F = T_a+P ~~ "504,498 cm"^2`

`"III. szabályos háromszög"`
`a = "17 cm"`

`T_a = sqrt(3)/4 a^2 = (289 sqrt(3))/4 ~~ "125,141 cm"^2`

Az a magasság amit az ötszögnél számoltunk az alapnál, itt a háromszög teljes magasságának harmada lesz:
`m/3 = (sqrt(3)/2 a)/3 = (17 sqrt 3)/6`

Az oldallapok magassága:
`m_o = sqrt(h^2+(m/3)^2) = sqrt(15^2+(17^2*3)/6^2) = (7 sqrt 183)/6 = "15,782 cm"`

`P = 3 T_o = 3*((a*m_o)/2) = (3*17*(7 sqrt 183)/6)/2 = (119 sqrt(183))/4 ~~ "402,451 cm"^2`

a) `V = (T_a*h)/3 = ((289 sqrt(3))/4*15)/3 = (1445 sqrt(3))/4 ~~ "625,703 cm"^3`

b) `F = T_a+P = (289 sqrt(3))/4+(119 sqrt(183))/4 ~~ "527,591 cm"^2`