Find AD length, if radius of both semicircle is 2cm
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AD is the diameter of a circle of radius 6 cm and AB=BC=CD. Semi-circles are drawn with AB and BD as diameters as shown in the figure. Find the perimeter and area of the shaded region.
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Solution
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We have AD= diameter of circle of radius 6cm=12cm
So, AB=BC=CD=
3
12
=4cm
BD=BC+CD=4+4=8cm
Hence required perimeter=arc of semicircle of radius 6cm+ arc of semicircle of radius 4cm+ arc of semicircle of radius 2cm
=(π×6+π×4+π×2)cm
=12πcm.
Required Area = area of semicircle with AD as diameter+area of semicircle with AB as diameter−area of semicircle with BD as diameter.
=
2
1
×
7
22
×6
2
+
2
1
×
7
22
×2
2
−
2
1
×
7
22
×4
2
=
2
1
×
7
22
(6
2
+2
2
−4
2
)
=
7
264
cm
2
=37.71cm
2