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+S

S1为以AC为直径的半圆面积, S1=π * (AC/2) * (AC/2) * (1/2)
= (π/8) * AC * AC
S2为以BC为直径的半圆面积, S2=π * (BC/2) * (BC/2) * (1/2)
= (π/8) * BC * BC
S1+S2 =(π/8) * AC * AC + (π/8) * BC *BC
=(π/8) * (AC * AC + BC * BC) 条件一
因为在直角三角形ABC中,角ACB=90°,
所以 AB * AB= AC * AC + BC * BC 条件二
AB=4 条件三
由条件一二三可知
S1+S2 =(π/8) * (AC * AC + BC * BC)
=(π/8) * AB * AB
=(π/8) * 4 * 4
=2π