Find the area of the square that can be inscribed in a circle of radius 6 cm.


Answer:

72 cm2

Step by Step Explanation:
  1. 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.
    O A B C D


    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
  2. Using Pythagores' theorem in ABC, we have AB2+BC2=AC2AB2+BC2=(12)2 [AC is the diagonal of the square.] AB2+AB2=144 [Sides of a square are equal.] 2AB2=144AB2=72
  3. We know,  Area of the square =Side2 Area of the square =AB2=72 cm2
  4. Thus, the area of the square that can be inscribed in a circle of radius 6 cm is 72 cm2.

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