①
`h = sz * 2.4`
`T = 6000 = h * sz = sz * 2.4 * sz = sz^2 * 2.4`

`sz^2 * 2.4 = 6000`
`sz^2 = 6000 // 2.4 = 2500`
`sz = sqrt(2500) = 50`

`h = sz * 2.4 = 50 * 2.4 = 120`

`K = 2 * (h + sz) = 2 * (120 + 50) = 2 * 170 = 340`

`"kerítés" = K - "kapu" = 340 - 5 = color(red)335 \ m`

Ellenőrzés:
`T = h * sz = 120 * 50 = 6000`

③
`T = "alap" * "magasság" = pi * r^2 * h = pi * 2^2 * 5 = pi * 20 ~~ color(red)62.83 \ cm^3`
`F = "alap" * 2 + "palást" = pi * r^2 * 2 + 2 * pi * r * m = pi * 2^2 * 2 + 2 * pi * 2 * 5 = pi * 8 + pi * 20 = pi * 28 = color(red)87.96 \ cm^2`

④
`"palást" = pi * r^2 * alpha / 360 = pi * 9^2 * 120 / 360 = pi * 81 * 1 / 3 = pi * 27 ~~ 84.82`
`K_"alap" = "palást ívhossza" = pi * 2 * r * alpha / 360 = pi * 2 * 9 * 120 / 360 = pi * 18 * 1 / 3 = pi * 6 ~~ 18.85`
`r_"alap" = K_"alap" / (pi * 2) = (pi * 6) / (pi * 2) = 3`
`F = "alap" + "palást" = pi * r_"alap"^2 + pi * 27 = pi * 3 + pi * 27 = pi * 30 ~~ color(red)94.25`

⑤
`"alap átló" = sqrt("alap él"^2 / 2) = sqrt(16^2 / 2) ~~ 11.31`
`"magasság" = sqrt("oldal él"^2 - "alap átló"^2) = sqrt(12^2 - 16^2 / 2) = sqrt((2 * 12^2 - 16^2) / 2) = sqrt(32 / 2) = sqrt(16) = 4`
`T = "alap" * "magasság") / 3 = (16 * 16 * 4) / 3 = 1024 / 3 ~~ color(red)341.33`