Question

ABCD is a square with side 2 root 2 cm and inscribed ina circle find the ar of shaded region

Answer 1

Solution:-

The area of the shaded region will be 4.56 cm²

Step-by-step explanation:

Given the side of the square = a = 2√2 = √8 cm

=> Area of the square = side² = a² = 8 cm²

We know that the length of the diagonal of a square is given by,

d = a√2

=> d = √8 x √2 = √16 = 4 cm

Since the square is inscribed in a circle, hence the diagonal of the square will be the diameter of the circle,

=> radius = d/2 = 4/2 = 2 cm

Area of the circle = πr²

= 3.14 x 2²

= 12.56 cm²

Hence the area of the shaded region will be

Area of circle - Area of the square

= 12.56 - 8

= 4.56 cm²

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@GauravSaxena01

Answer 2

Shaded area = 4.56 cm²

Step-by-step explanation:

Given ABCD is a square.

Side of square = $2\sqrt2$ cm

Area of square = side × side

                         $=2\sqrt2\times 2\sqrt2$

Area of square = 8 cm²

Diagonal = $\sqrt{ (2\sqrt{2} )^2+(2\sqrt{2} )^2}$

               = $\sqrt{8 + 8}$

               $=\sqrt{16}$

Diagonal = 4 cm

Diameter of circle = Diagonal of square

Diameter of circle = 4 cm

∴ Radius of circle = 2 cm

Area of circle = πr²

                      = 3.14 × 2²

Area of circle = 12.56 cm²

Shaded area = Area of circle - Area of square

                      = 12.56 cm² - 8 cm²

Shaded area = 4.56 cm²

To learn more...

1. ABCD is a square with Side 2 root 2 cm and inscribed in a circle find the area of the shaded region

https://brainly.in/question/8619705

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

https://brainly.in/question/8916178