Answer:
11.28 in²
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
_____
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.