如图,ABC是等腰直角三角形,D是圆周的中点,BC是半圆的直径,已知AB=BC=10厘米,那么阴影部分面积是?

如图,ABC是等腰直角三角形,D是圆周的中点,BC是半圆的直径,已知AB=BC=10厘米,那么阴影部分面积是?
如图,ABC是等腰直角三角形,D是圆周的中点,BC是半圆的直径,已知AB=BC=10厘米,那么阴影部分面积是?

如图,ABC是等腰直角三角形,D是圆周的中点,BC是半圆的直径,已知AB=BC=10厘米,那么阴影部分面积是?
连接CD,BD,OD
整个图形的面积
=等腰直角三角形ABC的面积+半圆的面积
=(10*10/2)+3.14*(10/2)*(10/2)/2
=50+39.25
=89.25平方厘米
阴影部分的面积
=整个图形的面积-三角形ACD的面积-拱形CD的面积
=整个图形的面积-三角形ACD的面积-二分之一的半圆面积+三角形COD的面积
等腰直角三角形ABC,角ACB=45度,AC=10倍根号2
D是圆周的中点,BC是半圆的直径,
所以三角形BCD也是等腰直角三角形,CD=5倍根号2,角BCD=45度
所以角ACD=角ACB+角DCB=45+45=90度
所以三角形ACD是直角三角形,它的面积=(5倍根号2)*(10倍根号2)/2=50平方厘米
二分之一半圆的面积=3.14*(10/2)*(10/2)/4=19.625
三角形COD也是等腰直角三角形,CO=OD==5,其面积=5*5/2=12.5,所以
阴影部分的面积
=整个图形的面积-三角形ACD的面积-二分之一的半圆面积+三角形COD的面积
=89.25-50-19.625+12.5
=32.125平方厘米

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