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

**SOLUTION**

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**Draw altitude to side . Because is a triangle with a hypotenuse of length 2 inches, .

Area of

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.