Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

geometry intermediate

Problem

A decorative arrangement of floor tiles forms concentric circles, as shown in the figure to the right. The smallest circle has a radius of 2 feet, and each successive circle has a radius 2 feet longer. All the lines shown intersect at the center and form 12 congruent central angles. What is the area of the shaded region? Express your answer in terms of .
problem
Solution
The smallest circle has radius 2, so the next largest circle has radius 4. The area inside the circle of radius 4 not inside the circle of radius 2 is equal to the difference: This area has been divided into twelve small congruent sections by the radii shown, and the shaded region is one of these. Thus, the area of the shaded region is:
Final answer
\pi