Area of quadrilateral

圖片參考：http://i1096.photobucket.com/albums/g340/pingshek/2011-06-22.png


http://i1096.photobucket.com/albums/g340/pingshek/2011-06-22.png

2011-06-22 15:19:18 補充：
Alt. method:

PQ: x - y + 10 = 0
PQ = √[(8 - 4)² + (-2 +6)²] = 4√2

In ΔPQR, altitude from R = |(- 8 - 10 + 10|/√(1² + 1²) = 8/√2
Area of ΔPQR = (1/2)*(4√2)*(8/√2) = 16

In ΔMQP, altitude from M = |(-3 - 5 + 10|/√(1² + 1²) = 2/√2
Area of ΔMQP = (1/2)*(4√2)*(2/√2) = 4

Area of PRQM = 16 + 4 = 20

2011-06-22 15:25:39 補充：
Using integration:

RQ: y = f(x)
RP: y = g(x)
PM: y = h(x)
MQ: y = j(x)
[Find f(x), g(x), h(x), j(x) by yourself.]



Area of PRQM
= ∫(-8 to -6) [f(x) - g(x)]dx + ∫(-6 to -3) [f(x) - h(x))dx + ∫(-3 to -2) [f(x) - j(x)]dx
= 20