if the perimeter of the shaded region is 132 cm, find the area of the shaded region
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Area of Shaded region = 693 cm² if the perimeter of the shaded region is 132 cm
Step-by-step explanation:
Let say AC = 4a cm
Then AB = BC = 2a cm
Radius of bigger Semicircle = 4a/2 = 2a cm
Radius of smaller circle = 2a/2 = a cm
Perimeter = π2a + πa + πa = 4πa
4πa = 132
=> 4(22/7)a = 132
=> 4a = 42
AC = 42 cm
AB = BC = 21 cm
Area of Shaded region = (1/2) π (2a)² - (1/2)πa² + (1/2)πa²
= (1/2) π (21)²
= (22/7) (21)² /2
= 693 cm²
Area of Shaded region = 693 cm²
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