Question

in the given figure find the area of shaded region​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, as per the given question we have to find the area of shaded region. Clearly from the given figure,

• ABCD is a rectangle in the circle.

According to the question,

→ Area of shaded region = Area of circle - Area of rectangle

Formulae to use :

★ Area of rectangle = Length × Breadth

★ Area of circle = πr²

Here, length and breadth of the rectangle are given.

• Length = AC = 8 cm
• Breadth = AB = 6 cm

Note : Diagonal of the rectangle (BC) is the diameter (BC) of the circle. So, we'll find the diameter first and divide it with 2 to find the radius of the circle. After that, by putting the values, we'll find the area of the circle.

• At last, we'll subtract the area of the rectangle from area of the circle to get our answer.

$\Large {\underline { \sf {Explication \: of \: Steps :}}}$

★ Area of shaded region = Area of circle - Area of rectangle

$\underline{\small \sf {\maltese \; \; \; Finding \: area \: of \: circle : \; \; \; }}$

• Here, diagonal of the rectangle ABCD is the diameter of the circle.

→ Diagonal of ABCD = Diameter of the circle

→ BC = √(length² + breadth²)

→ BC = √{(AC)² + (AB)²}

→ BC = √{(8)² + (6)²} cm

→ BC = √(64 + 36) cm

→ BC = √100 cm

→ BC = 10 cm [Diameter of the circle]

Let's find out radius because we need radius to calculate area of the circle.

→ Diameter = 2 × Radius

→ $\sf \dfrac{Diameter}{2}$ = Radius

→ $\sf \dfrac{10}{2}$ cm = Radius

→ 5 cm = Radius

★ Area of circle = πr²

→ Area of circle = 3.14 × (5)² cm²

→ Area of circle = 3.14 × 5 × 5 cm²

→ Area of circle = 3.14 × 25 cm²

→ Area of circle = 78.5 cm²

$\underline{\small \sf {\maltese \; \; \; Finding \: area \: of \: rectangle : \; \; \; }}$

★ Area of rectangle = Length × Breadth

→ Area of ABCD = 8 cm × 6 cm

→ Area of ABCD = 48 cm²

$\underline{\small \sf {\maltese \; \; \; Finding \: area \: of \: shaded\: region : \; \; \; }}$

★ Area of shaded region = Area of circle - Area of rectangle

→ Area of shaded region = ( 78.5 - 48 ) cm²

→ Area of shaded region = 30.5 cm²

Hence, we got the answer !