Question

ABCD is the diameter of circles of radius 6cm. the lengths AB, BC, and CD are equal. semicircles drawn on AB and BD as diameter. find the perimeter and area of the shaded region​

Answer 1

Answer:

Hey Mate

Hope it may help you

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

Hope u understand