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.

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About mvtrinh

Retired high school math teacher.
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