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.
OR
OR..
.​

Answer 1

Answer:

Area of Shaded region = 224 cm²

Step-by-step explanation:

Perimeter of circle = 88 cm

Perimeter of circle = 2 π  R

R = Radius of circle

π = 22/7

=> 2 * (22/7) * R  = 88

=> R = 14 cm

Area of circle = πR² =  (22/7) * 14² = 616 cm²

Diameter of Circle = 2 * Radius = 28 cm

Diagonal of Square = Diameter of circle = 28 cm

Side of Square = 28/√2  = 14√2 cm

Area of Square = (14√2)² = 392 cm²

Area of Shaded region = 616 - 392  = 224 cm²

Answer 2

Step-by-step explanation:

perimeter of the circle=2πr=88

r=88/(2×22/7)=14cm....[1]

length of diagonal of square=2r

let side of square=a

length of diagonal=(2a^2)^(1/2)

4r^2=2a^2

a=(✓2)r

a=14✓2

area of square=392

area of circle not in the square =(22/7)×14×14-392

=616-392

=224