如图所示 两个正方形的边长分别是a,b 且a>b （1）用a,b表示阴影部分的面积S

Question

（2）如果a+b=10,ab=20,求阴影部分的面积S的值。

Answer 1

1. 阴影面积=a²ï¼‹b²-(a²Ã·2＋b·(a+b)÷2)
=a²ï¼‹b²-1/2(a²+ab+b²)
=a²/2+b²/2-ab/2
=1/2(a²ï¼‹b²-ab)
2. 面积
=1/2[(a+b)²-3ab]
=1/2[10²-3×20]
=1/2×40
=20

Answer 2

S=a²+b²-1/2a²-1/2b(a+b)
=1/2a²-1/2ab+1/2b²
S=1/2a²-1/2ab+1/2b²
=1/2(a²-ab+b²)
=1/2(a+b)²-3/2ab
=50-30
=20