>>303

　AB = CD = p,
　AC = BD = q,
AD = BC = r,
とすると
　xx = (pp-qq+rr)/2,
　yy = (pp+qq-rr)/2,
　zz = (-pp+qq+rr)/2,
さて、
↑PQ = (1/6)(-2x，y，3z)
　↑PR = (1/3)(x，0，3z)
　PQ×QR = (1/18)(3yz，9zx，-xy),

△PQR = (1/2) | PQ×QR |
　= (1/36) | (3yz，9zx，-xy) |
　= (1/36)√{(3yz)^2 + (9zx)^2 +(xy)^2}
　= (1/36)√(-89p^4 -73q^4 +71r^4 +162ppqq +2qqrr +18rrpp)

(p,q,r) = (7,8,9)，△ = (2/9)√2121 = 10.23429239081729
(p,q,r) = (8,9,7)，△ = (2/9)√903 = 6.6777685339185419
(p,q,r) = (9,7,8)，△ = (2/9)√(9･119) = 7.2724747430904763
(p,q,r) = (7,9,8)，△ = (2/9)√1203 = 7.7076200871220558
(p,q,r) = (9,8,7)，△ = (2/9)√(9･89) = 6.28932075470440254
(p,q,r) = (8,7,9)，△ = (2/9)√2091 = 10.161656324598823