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I assume an equilateral triangle and its circumscribed circle. The centre of the triangle and circle are the same point and the radius is from the centre to a vertex. Joining two radii to vertices we get an isosceles triangle with angle at the centre=120 degrees (360/3) and the equal angles are 30 degrees. The isosceles triangle can be divided into two back-to-back right-angled triangles with hypotenuse (radius) = 4". The height of the right triangle is 4sin30=2 inches and the base = 4cos30 = 2√3 inches. The area of one such triangle = 2√3. There are 6 right triangles formed by the radii and vertices, so the area of the equilateral triangle is 6*2√3=12√3=20.78 sq in (approx).

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