Question

30. In the figure ABCD is a square, whose vertices lie on the circle. Find the area of the shaded region, if
the perimeter of the circle is 88cm.​

Answer 1

ANSWER :

284 cm^2

Step-by-step explanation:

Please refer to the image.

Answer 2

Answer:

223.75 cm²

Step-by-step explanation:

In the figure ABCD is a square inside the circle whose vertices lie on the circle.

The perimeter of the circle = 88 cm

                                      2πr = 88

                                      $r=\dfrac{88\cdot 7}{2\cdot 22}$

                                      $r=14$ cm

Diameter of circle = 2r

                              = 2×14

                              = 28 cm

Diameter of circle is equal to diagonal of square.

Let side of square be x cm

Length of diagonal $=x\sqrt{2}$

So, $x\sqrt{2}=28$

$x=14\sqrt{2}\ cm$

Area of square $=x^2$

Area of square, $A_S=(14\sqrt{2})^2=392\ cm^2$

Area of circle $=\pi r^2$

Area of circle, $A_C=\pi \cdot 14^2=615.75\ cm^2$

Area of shaded region = Area of circle - Area of square

                                       = 615.75 - 392

                                       = 223.75 cm²