Question

八边形ABCDEFGH其顶点坐标依次为A(1,0)B(2,0)C(6,3)D(7,5)E(5,9)F(3,8)G(0,5

Answer 1

多边形面积,用向量

2S = A x B + B x C + C x D + D x E + E x F + F x G + G x H + H x A

其中 A,B...分别为向量 (1,0),(2,0),.x 表示他们的矢量积 (在 z 方向上的投影)

A x B = 1 * 0 - 0 * 2 = 0

B x C = 2 * 3 - 0 * 6 = 6

C x D = 6 * 5 - 3 * 7 = 9

D x E = 7 * 9 - 5 * 5 = 38

E x F = 5 * 8 - 3 * 9 = 13

F x G = 3 * 5 - 8 * 0 = 7

G x H = 0 * 2 - 5 * 0 = 0

H x A = 0 * 0 - 2 * 1 = -2

2S = 0 + 6 + 9 + 38 + 13 + 7 + 0 - 2 = 71

S = 71/2