Question

In Figure, ABCD is a square with side 2√2 cm and inscribed in a circle. Find the area of the shaded
region
(User = 3.14)​

Answer 1

Answer:

Answer:

4.56 cm²

1.14 cm²

Step-by-step explanation:

Abcd is a square with side 2√2 cm and inscribed in a circle find the area of the shaded region π= 3.14

Diagonal of square = √((2√2)² + (2√2)²) = √ (8 + 8) = √16 = 4cm

Diameter of Circle = 4 cm

Radius of Circle = 4/2 = 2cm

Area of circle = π r² = 3.14 * (2)² = 12.56 cm²

Area of square = (2√2)² = 8 cm²

Area of circle - Area of square = 12.56 - 8 = 4.56 cm²

Area of one shaded portion = 4.56/4 = 1.14 cm²

AC = √72

AC = 6√2 cm

Thus the diameter of the circle is 6√2 cm .

Radius = 3√2 cm

Thus

Shaded area = Area of a circle - Area of a square

= 3.14 × 3√2 × 3√2 - 6²

= 3.14 × 9 × √2 × √2 - 36

(As √2 × √2 = 2 , 6² = 36 )

= 3.14 × 9 × 2 - 36

= 56.52 - 36

= 20.52 cm²

Therefore the area of the shaded area is 20.52 cm² .