Question

4*8长方形里面有一个直径8的半圆，求阴影面积

Answer 1

由题意可得AF=FB=4，做EG垂直AF于G。求AE=4根号5/5，EG=0.8 AG=1.6 GF=2.4.连接EF，求EF对应圆心角度（或占半圆比例）由圆心连接OE至AF交于H。可知∠FOH对应角为arctan=3/4。求AEF面积-EF弧形面积。

S阴=S△ABC+S△OEC-S扇形OEC-S角FBC
=4*8/2+1/2*4*4*(sinα-α)-(8*8-π*4*4)/4
=16+8*(sin(π-2β)-(π-2β))-(16-4π)
=8*4/5-4π+16β=6.4-8[π/2-atan(4/3)]
=6.4-8atan(3/4)=4*4/2*[4/5-acos(4/5)]≈1.25199

Answer 2

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