From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. T

Question

From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is

Accepted Answer

88 + 12π. Area of the semicircle with AB as a diameter = 1 2 ∗ π ∗ ( A B 2 4 ) \dfrac{1}{2}*\pi*(\dfrac{AB^2}{4}) 2 1 ​ ∗ π ∗ ( 4 A B 2 ​ ) ⇒ \Rightarrow ⇒ 1 2 ∗ π ∗ ( A B 2 4 ) \dfrac{1}{2}*\pi*(\dfrac{AB^2}{4}) 2 1 ​ ∗ π ∗ ( 4 A B 2 ​ ) = 72 ∗ π 72*\pi 72 ∗ π ⇒ \Rightarrow ⇒ A B = 24 c m AB = 24 cm A B = 24