题目内容
如图,在Rt△ABC中,∠ACB=90°,AC=BC=1,将Rt△ABC绕A点逆时针旋转30°后得到Rt△ADE,点B经过的路径为
,则图中阴影部分的面积是_________.



先根据勾股定理得到AB=
,再根据扇形的面积公式计算出S扇形ABD,由旋转的性质得到Rt△ADE≌Rt△ACB,于是S阴影部分=S△ADE+S扇形ABD-S△ABC=S扇形ABD
解答:解:∵∠ACB=90°,AC=BC=1,
∴AB=
,
∴S扇形ABD=
.
又∴Rt△ABC绕A点逆时针旋转30°后得到Rt△ADE,
∴Rt△ADE≌Rt△ACB,
∴S阴影部分=S△ADE+S扇形ABD-S△ABC=S扇形ABD=
.
故答案为:
.

解答:解:∵∠ACB=90°,AC=BC=1,
∴AB=

∴S扇形ABD=

又∴Rt△ABC绕A点逆时针旋转30°后得到Rt△ADE,
∴Rt△ADE≌Rt△ACB,
∴S阴影部分=S△ADE+S扇形ABD-S△ABC=S扇形ABD=

故答案为:


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