## Yellow Star

The four circles in the figure below each have a radius of 5 units. The centers of each circle form a square. If you use 3.14 as the approximate ratio of a circle’s circumference to its diameter, what is the area of the interior [yellow] black star region?
Source: mathcontest.olemiss.edu 9/25/2006

SOLUTION

Area of interior black star region = Area of square $-$ Area of 4 circle quarters.
= Area of square $-$ Area of 1 circle
$=10^2-\pi \times 5^2$
$=10^2-3.14\times 25$
$=100-78.5$
$=21.5$ square units

Answer: $21.5$ square units.