10. ABCD is a diameter of a circle of radius 6 cm.The length AB, BC and CD are equal.les are drawn on AB and BD as diameters as shown in the given figure. The shaded region of the area is found.
Answers
Answer:
Area of shaded region = 12π cm²
Step-by-step explanation:
Since, Length of AB, BC and CD are equal
Radius of circle = 6 cm
Now, AD = 2 × 6 = 12 cm
⇒ AB + BC + CD = 12
⇒ 3AB = 12
⇒ AB = 4 cm
⇒ AB = BC = CD = 4 cm
Radius of semicircle AB = 2 cm
Radius of semicircle BD = 4 cm
Radius of semicircle AD = 6 cm
Area of the shaded region = Area of semicircle ( AB + AD ) - Area of semicircle(BD)
⇒ Area of shaded region = 0.5π( 2² + 6² ) - 0.5π(4²)
⇒ Area of shaded region = 0.5π (4 + 36) - 0.5π × 16
⇒ Area of shaded region = 20π - 8π
⇒ Area of shaded region = 12π cm²
Answer:
In the given that AD = 12cm
and AB=BC=CD=1/3 AD=4cm.
BD = (12-4)cm = 8 cm.
therefore, required area = ( area of semicircle of diameter AD) + ( area of semicircle of diameter AB ) - ( area of semicircle of diameter BD)
={(1/2*22/7*6*6) + ( 1/2*22/7*2*2) - (1/2*22/7*4*4)}cm^2
=( 396/7+44/7-176/7)cm^2
=(396+44-176/7)cm^2
=264/7cm^2
=37.71cm^2
hence, the required area is 37.7 1 cm^2
