Question

在平面直角坐标系中,四边形ABCD各顶点的坐标分别是A(-3,4),B(-4,-2),C(2,0)、D（2,3）,且AB

Answer 1

C,D的横坐标相同,CD与x轴垂直.

从A向与x轴做垂线,垂足为F(-3,0)

梯形ADCF的面积a = (1/2)(AF + CD)*FC = (1/2)(4 + 3)(2 + 3) = 35/2

三角形BCE的面积b = (1/2)|B的纵坐标|*EC = (1/2)*2*(2 + 11/3) = 17/3

三角形AEF的面积c = (1/2)FA*EF = (1/2)*4*(-3 + 11/3) = 4/3

四边形ABCD的面积 = a + b + c = 35/2 + 17/3 + 4/3 = 49/2