Thread: geometry of circle

If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square

Originally Posted by Rimas

If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square

Okay is the diamter of the disk?

We know that,

Thus,

Thus,

That means the diamter of the circle is twice as much,

But the diamter of the circle is the hypotenuse of the square.

The square creates a 45,45,90 triangle. Thus, the side of the square is,

That means the area of the square is,

Originally Posted by Rimas

If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square

See diagram.

Now let r be the radius of the circle then:

36 pi = pi r^2,

and so r=6 cm.

Therefore the side of the square is 12 cm, and its area is
144 sq cm.

RonL