Question

Find the area of the square inscribed in a circle of radius 10 cm
.

Answer 1

Let ABCD be the square th
at is inscribed inside a circle having the centre at O.Now, 
radius of the circle, r = 10 units
So, diameter of the circle, AC = 2r = 20 units
Now, 
length of diagonal of square ABCD, 
AC = 20 unitsWe 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 ∆ABC,
 we haveAC2 = AB2 + BC2   [Pythagoras theorem]⇒(20)2 = AB2+AB2⇒2AB2 = 400⇒AB2 = 200Now, area of square ABCD = (side)2 = AB2 = 200 square units

Answer 2

Step-by-step explanation:

Square is inscribed in a circle.

So, the diagonal of square is the diameter of circle

Radius of circle = 10 cm

Diameter = 20 cm

Diagonal of square = 20 cm

We know that: Diagonal of a square = side*√2

20 = side *√2

side = 20/√2 = 10*2/√2 = 10*√2*√2/√2 = 10√2 cm

Area = side² = [10√2]² = 100*2 = 200 cm²