Question

In the given figure, ABCD is a rectangle
inscribed in a circle having length 8 cm and
breadth 6 cm. If n = 3.14 then the area of the
shaded region is
​

Answer 1

Answer:

answer is 30.5cm .

join AC.

now ,AC is the diameter of the circle

AC2 = AB2 + BC2 [ by pythagoras ' theorem ]

=> AC^2 = {(8)^2+(6)^2} cm^2

=>AC^2 = ( 64 + 36 ) CM^2

=> AC^2 = 100cm^2

.: radius of the circle = 10/2 cm

= 5 cm

now,

area of the shaded region = area of the circle with radius  5cm - area of rectangle ABCD

= ( 3.14 x 5 x 5 )  -( 8x6) cm^2

= (314/100 x 25) - 48 cm^2

=(157/2 - 48) cm^2

= 61/2 cm^2

30.2 cm^2

Explanation : please thank and mark me brainlist !!

Answer 2

Explanation:

In order to Find the Area of the Shaded Region : First We need to Find the Area of the Circle and Find the Area of Rectangle and then Subtract Area of Rectangle from Area of the Circle.

First Let us find the Area of the Circle :

In order to find the Area of the Circle, We require the radius of the Circle. But, the Radius of the Circle is not mentioned.

Then, How to Find the Radius of the Circle?

By Looking at the Diagram, We can Notice that the Diagonal of the Rectangle is the Diameter of the Circle.

So, We need to find the Diagonal of the Rectangle.

We know that Diagonal of a Rectangle divides the Rectangle into two congruent Right angled Triangles, where Diagonal is the Hypotenuse and Length and Breadth of the Rectangle are legs.

Given : Length = 8 cm and Breadth = 6 cm

⇒ (Length)² + (Breadth)² = (Diagonal)²

⇒ (Diagonal)² = 8² + 6²

⇒ (Diagonal)² = (64 + 36) = 100

⇒ Diagonal = 10 cm

⇒ Diameter of the Circle = 10 cm

⇒ Radius of the Circle = 5 cm

We know that Area of Circle is given by : πr²

⇒ Area of the given Circle = 3.14 × 25 = 78.5 cm²

We know that Area of Rectangle is given by : Length × Breadth

⇒ Area of the given Rectangle = 8 × 6 = 48 cm²

⇒ Area of Shaded Region = Area of Circle - Area of Rectangle

⇒ Area of Shaded Region = (78.5 - 48) = 30.5 cm²