From a rectangle ABCD of area 812 cm2, a semicircular part with diamet

1.	From a rectangle ABCD of area 812 cm2, a semicircular part with diameter CD and area 98π cm2 are removed, find the perimeter of the remaining figure.1. 125 cm2. 135 cm3. 130 cm4. 164 cm
Answer» Correct Answer - Option 3 : 130 cm Given - area of rectangle = 812 cm², area of semicircle = 98π cm² Formula used - area of rectangle = length × breadth area of semicircle = (1/2) × π × radius² Solution - Let the radius of the semi - circle is r cm. ⇒ (1/2) × π r² = 98π ⇒ r² = 196 ⇒ r = 14 cm ⇒ diameter of the semi - circle = 28 cm ⇒ diameter of semi - circle = side of rectangle CD = 28 cm ⇒ area of rectangle = 812 cm² ⇒ BC × CD = 812 ⇒ BC × 28 = 812 ⇒ BC = 29 cm ⇒ We have to find perimeter of remaining figure so, ⇒ perimeter = AB + BC + AD + (1/2) × perimeter of the circle ⇒ perimeter = 28 + 29 + 29 + (1/2) × (2πr) ⇒ perimeter = 58 + 28 + (22/7) × 14 ⇒ perimeter = 130 cm ∴ perimeter of remaining figure = 130 cm.

From a rectangle ABCD of area 812 cm2, a semicircular part with diameter CD and area 98π cm2 are removed, find the perimeter of the remaining figure.1. 125 cm2. 135 cm3. 130 cm4. 164 cm

Answer» Correct Answer - Option 3 : 130 cm

Given -

area of rectangle = 812 cm², area of semicircle = 98π cm²

Formula used -

area of rectangle = length × breadth

area of semicircle = (1/2) × π × radius²

Solution -

Let the radius of the semi - circle is r cm.

⇒ (1/2) × π r² = 98π

⇒ r² = 196

⇒ r = 14 cm

⇒ diameter of the semi - circle = 28 cm

⇒ diameter of semi - circle = side of rectangle CD = 28 cm

⇒ area of rectangle = 812 cm²

⇒ BC × CD = 812

⇒ BC × 28 = 812

⇒ BC = 29 cm

⇒ We have to find perimeter of remaining figure so,

⇒ perimeter = AB + BC + AD + (1/2) × perimeter of the circle

⇒ perimeter = 28 + 29 + 29 + (1/2) × (2πr)

⇒ perimeter = 58 + 28 + (22/7) × 14

⇒ perimeter = 130 cm

∴ perimeter of remaining figure = 130 cm.