Question

a square abcd is inscribed in a circle of radius 10 units. find the area of the circle,not include in the squar.

Answer 1

Remaining area = ar(Circle) - ar(ABCD)

ar(ABCD) = a²
Since, radius is 10 units.
a = 10√2 units

ar(ABCD) = 200 units

ar(Circle) = π(10)²
ar(Circle) = 100π

remaining area = 3.14(100) - 200
= 114 units.

Answer 2

Hello,
let's look at the image.

Let ABCD be the square that is inscribed inside a circle having the centre at O.
now, radius of the cirche,r=10 units
so,diameter of the circle:
AC=2r=2×10=20 units

Now,leght of diagonal of square ABCD,AC=20 units.

We know that each angle of a square is a right angle,
so ∠A=∠B∠C=∠D=90°
Also each side of the square is also equal.
So,Ab=BC=CD=AD.

in ΔABC,we have ,for Pythagoras theorem:
AC²=AB²+BC²;
20²=AB²+AB²;
2AB²=400;
AB²=200;

Now,area os square ABCD:
A(ABCD)=AB²=200 units²
we calculate thearea of circle:
Ac=πr²=3.14×10²=3.14×100=314 units²

we calculate the area of shade region:
A= Ac-A(ABCD)=314-200=114 units²

bye :-)