Question

AD is the diameter of a circle of radius 6 centimetre and AB is equal to BC is equal to CD. semi circles are drawn with AB and BD as diameter shown in the figure. find the perimeter and area of the shaded region

Answer 1

Perimeter of shaded region = perimeter of semicircle with diameter AD + perimemter of semicircle with diameter AB + perimeter of semicircle with diameter BD


as, AB=BC=CD
and
AB + BC+CD = diameter of the big circle = 6cm
3 AB = 6cm
AB = 2cm
similarly, BC and CD = 2cm


In the circle with AD as diameter,
then radius = 1/2(AD) = 3cm (as AD = 6cm)
perimeter of the whole circle = 2πr
perimeter of semicircle with diameter AD = (1/2) perimeter of the whole circle = πr
so, the perimeter of that semicircle becomes = 3π cm.




In semicircle with diameter AB = 2cm
radius = 1cm
Then, it's perimeter would be π cm.


Similarly, In the semicircle with diameter BD
BD = BC + CD = 2cm+2cm = 4cm
then, it's radius = 2cm
it's perimeter then becomes 2π cm.



Therefore , the primeter if shaded region becomes 3π + π + 2π = 6π cm.