SOLUTION: The area of a square is 72 cm. The area of the circle drawn on its diagonal is?

I can't tell what is meant by "the circle drawn on its diagonal".


THIS:OR THIS:

In either case we calculate s the length of a side of the square, 
using:

    A = s²
   72 = s²
  √72 = √s²
  √72 = s
√36·2 = s
  6√2 = s

If it's the first case we draw a horizontal diameter (in green) which is equal
in length to the side of the square, 6√2. and therefore each radius is half of 
that or 3√2



So to find the area of the circle we use:

A = pr2
A = p(3√2)2
A = p·32·(√2)2
A = p·9·2
A = 18p cm²
A ≈ 56.55 cm² 

But if it's the second way, then the diagonal is the diameter
of the circle, d:



We calculate d with the Pythagorean theorem:

d2 = (6√2)2 + (6√2)2
d2 = 2·(6√2)2 
d2 = 2·62(√2)2
d2 = 2·36·2
d2 = 144
 d = 12

And the radius is half the diameter, so the radius of the circle
is 6 cm.

To find the area of the circle we use:

A = pr2
A = p62
A = p·36
A = 36p cm²
A ≈ 113.1 cm²

The area of the circle in the second case is exactly twice
the area in the first case.  That is to say, the circle
circumscribed about a square has twice the area of the circle
inscribed in the square. 

Edwin