What is the area of a reuleaux triangle that has a diameter of 4 in.? round answer to the nearest hundredth.

  11.28 in²

Step-by-step explanation:

The area of a Reuleaux triange is given by ...

  A = (1/2)(π -√3)d² . . . . . where d is the diameter of the triangle.

For a triangle of diameter 4 in, the area is ...

  A = (1/2)(π -√3)(4 in)² = (π -√3)8 in² ≈ 11.28 in²

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A Reuleaux triangle is the shape of smallest area that has a constant diameter. The diameter of the shape is the radius of each of the arcs between the vertices of the inscribed equilateral triangle.

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