2017 AMC 8 Problems/Problem 25
In the figure shown, and are line segments each of length 2, and . Arcs and are each one-sixth of a circle with radius 2. What is the area of the region shown?
Let the centers of the circles containing arcs and be and , respectively. Extend and to and . The area of the figure is equal to the area of equilateral triangle minus the combined area of the sectors of the circles. The area of is The combined area of the sectors is Our final answer is then