Question

ln 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

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

Answer 2

Area of shaded region=$224cm^2$

Step-by-step explanation:

Perimeter of circle=88cm

Circumference of circle=$2\pi r$

Where r=Radius of circle

Using the formula  and $\pi=\frac{22}{7}$

$88=2\times \frac{22}{7}\times r$

$r=\frac{88\times 7}{2\times 22}=14cm$

Area of circle=$\pi r^2$

Using the formula

Area of circle=$\frac{22}{7}\times (14)^2=616cm^2$

Diagonal of square=Diameter of circle=2r

Diagonal of square=$2\times 14=28cm^2$

Let x  be the side of square

In triangle ABC

$AC^2=AB^2+BC^2$

Using Pythagoras theorem

$(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

$x^2+x^2=(28)^2$

$2x^2=784$

$x^2=\frac{784}{2}=392$

Area of square=$x^2=392$

Where x= Side of square

Area of shaded region=Area of circle-area of square=616-392=224 square cm

#Learns more:

https://brainly.in/question/12425403