用4条边来表示梯形面积

王守恩

已知梯形 4 条边 = 4个不同正整数。 记梯形上底 = a, 左腰 = b, 右腰 = c, 下底 = d。
若用 a, b, c, d 来表示梯形最大面积。必有:  a < b < c < d,   c = b + 1。

1. Table[Maximize[{((d + a) Sqrt[((2 b + 1)^2 - (d - a)^2) ((d - a)^2 - 1)])/(4 (d - a)), 0 < a < b < d, a + 2 b + 1 + d == n}, {a, b, d}, Integers], {n, 121, 150}]

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a(10)——a(15)=a,b,c,d。 a(16)=a,b,d。
a(10)={1,2,3,4}
a(11)={1,2,3,5}
a(12)={1,2,4,5}
a(13)={1,3,4,5}
a(14)={2,3,4,5}
a(15)={2,3,4,6}
a(16)={1,4,6}
a(17)={2,4,6}
a(18)={3,4,6}
a(19)={3,4,7}
a(20)={2,5,7}
a(21)={3,5,7}
a(22)={4,5,7}
a(23)={4,5,8}
a(24)={3,6,8}
a(25)={4,6,8}
a(26)={5,6,8}
a(27)={5,6,9}
a(28)={4,7,9}
a(29)={5,7,9}
a(30)={5,7,10}
a(31)={6,7,10}
a(32)={5,8,10}
a(33)={6,8,11}
a(34)={6,8,11}
a(35)={7,8,11}
a(36)={6,9,11}
a(37)={7,9,11}
a(38)={7,9,12}
a(39)={8,9,12}
a(40)={7,10,12}
a(41)={8,10,12}
a(42)={8,10,13}
a(43)={9,10,13}
a(44)={8,11,13}
a(45)={9,11,13}
a(46)={9,11,14}
a(47)={8,12,14}
a(48)={9,12,14}
a(49)={9,12,15}
a(50)={10,12,15}
a(51)={9,13,15}
a(52)={10,13,15}
a(53)={10,13,16}
a(54)={11,13,16}
a(55)={10,14,16}
a(56)={11,14,16}
a(57)={11,14,17}
a(58)={12,14,17}
a(59)={11,15,17}
a(60)={12,15,17}
a(61)={12,15,18}
a(62)={13,15,18}
a(63)={12,16,18}
a(64)={13,16,18}
a(65)={13,16,19}
a(66)={14,16,19}
a(67)={13,17,19}
a(68)={13,17,20}
a(69)={14,17,20}
a(70)={14,17,21}
a(71)={14,18,20}
a(72)={14,18,21}
a(73)={15,18,21}
a(74)={15,18,22}
a(75)={16,18,22}
a(76)={15,19,22}
a(77)={16,19,22}
a(78)={16,19,23}
a(79)={17,19,23}
a(80)={16,20,23}
a(81)={17,20,23}
a(82)={17,20,24}
a(83)={18,20,24}
a(84)={17,21,24}
a(85)={18,21,24}
a(86)={18,21,25}
a(87)={19,21,25}
a(88)={18,22,25}
a(89)={19,22,25}
a(90)={19,22,26}
a(91)={20,22,26}
a(92)={19,23,26}
a(93)={20,23,26}
a(94)={20,27,27}
a(95)={19,24,27}
a(96)={20,24,27}
a(97)={20,24,28}
a(98)={21,24,28}
a(99)={20,25,28}
a(100)={21,25,28}
a(101)={21,25,29}
a(102)={22,25,29}
a(103)={21,26,29}
a(104)={22,26,29}
a(105)={22,26,30}
a(106)={23,26,30}
a(107)={22,27,30}
a(108)={23,27,30}
a(109)={23,27,31}
a(110)={24,27,31}
a(111)={23,28,31}
a(112)={24,28,31}
a(113)={24,28,32}
a(114)={25,28,32}
a(115)={24,29,32}
a(116)={25,29,32}
a(117)={25,29,33}
a(118)={26,29,33}
a(119)={25,30,33}
a(120)={26,30,33}
a(121)={26,30,34}
a(122)={27,30,34}
a(123)={26,31,34}
a(124)={26,31,35}
a(125)={27,31,35}
a(126)={27,31,36}
a(127)={27,32,35}
a(128)={27,32,36}
a(129)={28,32,36}
a(130)={28,32,37}
a(131)={29,32,37}
a(132)={28,33,37}
a(133)={29,33,37}
a(134)={29,33,38}
a(135)={30,33,38}
a(136)={29,34,38}
a(137)={30,34,38}
a(138)={30,34,39}
a(139)={31,34,39}
a(140)={30,35,39}
a(141)={31,35,39}
a(142)={31,35,40}
a(143)={32,35,40}
a(144)={31,36,40}
a(145)={32,36,40}
a(146)={32,36,41}
a(147)={33,36,41}
a(148)={32,37,41}
a(149)={33,37,41}
a(150)={33,37,42}

王守恩

这个问题有现实意义。梯形4条边(不等)的和=987654321,最大面积=?。

主帖类似给定一组平行边的等周多边形问题

可以参考帖子：[求助] 给定一个内角的等周多边形问题

已知 n 边形有一组平行边,  周长为 n,  求它的最大面积