如图,已知在RT△ABC中,角ABC=90°,AB=4,分别以AC、BC为直径作半圆,面积分别记为S1、S2,则S1+S2的值等于多少?

如图,已知在RT△ABC中,角ABC=90°,AB=4,分别以AC、BC为直径作半圆,面积分别记为S1、S2,则S1+S2的值等于多少?
如图,已知在RT△ABC中,角ABC=90°,AB=4,分别以AC、BC为直径作半圆,面积分别记为S1、S2,则S1+S2的值等于多少?

如图,已知在RT△ABC中,角ABC=90°,AB=4,分别以AC、BC为直径作半圆,面积分别记为S1、S2,则S1+S2的值等于多少?
知道AC^2+BC^2=AB^2=16
而S1=π（AC/2）^2/2=πAC^2/8
S2=πBC^2/8
所以
S1+S2=(π/8)(AC^2+BC^2)=2π.

八分之一乘以π再乘以AB的平方，就是2π。

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