梯形面积公式
1.求OB
易证：△AOB∽△DAE
所以有
注：部分线段长度为推导出（相似+梯形性质）
\[\int_{\frac{xz}{y-z} }^{\frac{xz}{y-z}+x } \frac{y-z}{x} x dx
=\frac{y-z}{x} \left [ \frac{\left ( \frac{xz}{y-z}+x \right )^2 }{2}+c-\frac{\left ( \frac{xz}{y-z}+x \right )^2 }{2}-c \right ]
= \frac{y-z}{x}\left [ \frac{x^2}{2}+\frac{x^2z}{y-z} \right ]
=\frac{xy-xz}{2}+xz
=\frac{xy+xz}{2}
=\frac{x\left ( y+z \right ) }{2}
\]