(2014?盐城)如图,在矩形ABCD中,AB=3,AD=1,把该矩形绕点A顺时针旋转α度得矩形AB′C′D′,点C′落

2025-05-14 06:14:25
推荐回答(1个)
回答1:

∵在矩形ABCD中,AB=

3
,AD=1,
∴tan∠CAB=
1
3
=
3
3
,AB=CD=
3
,AD=BC=1,
∴∠CAB=30°,
∴∠BAB′=30°,
∴S△AB′C′=
1
2
×1×
3
=
3
2

S扇形BAB′=
30π×(
3
)
2
360
=
π
4