Standardized tests will often ask you to find
the area of a circumscribed square.
To find the area of square IJKL, we need to know the
length of a side. Let's see if we can use the circumference of the inscribed
circle to find this measurement.
We know that we can figure out the circle's diameter and radius
from the circumference. How does this help? Well, the diameter of the
circle is the same length as each side. Because squares have parallel
sides, any line that is perpendicular to IL and JK
and that connects these two lines will have the same length
as IJ. The diameter of Circle O is one such line.
Circumference equals 
.
Since Circle O has a circumference of 8
,
its diameter is 8. So, each side of the square is also 8.
Therefore, the area of IJKL is 
.
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