请计算图中阴影部分面积
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请计算图中阴影部分面积
![](http://img.wesiedu.com/upload/5/31/531971f350d1f5ce0307245a1d9634b4.jpg)
![](http://img.wesiedu.com/upload/5/31/531971f350d1f5ce0307245a1d9634b4.jpg)
![请计算图中阴影部分面积](/uploads/image/z/4236498-18-8.jpg?t=%E8%AF%B7%E8%AE%A1%E7%AE%97%E5%9B%BE%E4%B8%AD%E9%98%B4%E5%BD%B1%E9%83%A8%E5%88%86%E9%9D%A2%E7%A7%AF)
用坐标法
设矩形为OABC,
令O(0,0),A(0,6),B(8,6),C(8,0),OA中点P(0,3),AB中点Q(4,6).
易得L(PB):y-3 = x/4
L(OQ):y = 3x/2
两直线交点为:K(12/5 ,18/5),∴设KT⊥x轴于T(12/5 ,0)
∴S阴 = S△OKT + S梯KTCB
= (1/2)·(12/5)·(18/5) + (1/2)·(8 - 12/5)·(6 + 18/5)
= (108/25) + (672/25)
= 780/25
= 31.2
设矩形为OABC,
令O(0,0),A(0,6),B(8,6),C(8,0),OA中点P(0,3),AB中点Q(4,6).
易得L(PB):y-3 = x/4
L(OQ):y = 3x/2
两直线交点为:K(12/5 ,18/5),∴设KT⊥x轴于T(12/5 ,0)
∴S阴 = S△OKT + S梯KTCB
= (1/2)·(12/5)·(18/5) + (1/2)·(8 - 12/5)·(6 + 18/5)
= (108/25) + (672/25)
= 780/25
= 31.2