Question

In the given figure ABCD is a square with side 6 cm. Find the area of the shaded region.

Answer 1

I have Named the Centre as O.

Check out Full Process in Pic.

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Answer 2

Answer:

The area of the shaded area is 20.52 cm² .

Step-by-step explanation:

Formula

Area of a square = a²

$Area\ of\ a\ circle = \pi r^{2}$

Where a is the side of the square and r is the radius of the circle .

As given

ABCD is a square with side 6 cm.

Now first find out the radius of the circle.

In ΔABC

AC² = AB² + BC²

Now by using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

(As AB = BC = 6 cm)

AC² = 6² + 6²

AC² = 36 + 36

AC² = 72

AC = √72

AC = 6√2 cm

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

$Radius = \frac{Diameter}{2}$

$Radius = \frac{6\sqrt{2}}{2}$

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 .