Find the area of the square that can be inscribed in a circle of radius 6 cm.
Answer:
72 cm2
- Let us draw a circle with O as a center and radius 6 cm.
Now, let us draw a square ABCD inside the circle. We see that the diagonal of the square is equal to the diameter of the circle.
Radius of the circle = 6 cm
So, diameter of the circle =2× Radius =2×6 cm=12 cm
Therefore, diagonal of the square =12 cm - Using Pythagores' theorem in △ABC, we have AB2+BC2=AC2⟹AB2+BC2=(12)2 [AC is the diagonal of the square.] ⟹AB2+AB2=144 [Sides of a square are equal.] ⟹2AB2=144⟹AB2=72
- We know, Area of the square =Side2⟹ Area of the square =AB2=72 cm2
- Thus, the area of the square that can be inscribed in a circle of radius 6 cm is 72 cm2.