The tessellated figure below consists of 3 equal arcs in an equilateral triangle. Each side measures 2 inches. What is the area of the region labeled ?
Source: Julia Robinson Mathematics Festival
Draw altitude to side . Because is a triangle with a hypotenuse of length 2 inches, .
Each arc lies on a circle of radius 1 inch centered at one of the three vertices of . Each arc forms a sector with a central angle measuring . The three sectors if placed contiguously next to each other would therefore form a semicircle.
Area of the three sectors =
Area of region = area of area of the three sectors
Answer: square inches.