ABCD is the diameter of circle of radius
6cm. The lengths AB, BC and CD are
equal. Semicircles are drawn on AB and
BD as diameters. Find the perimeter and
the Area of the shaded region.
Answers
Answer:
12π cm²
Step-by-step explanation:
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
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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
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