What radius of a circle is required to inscribe an equilateral triangle with an area of 15.588 in2 and an altitude of 5.196 in? (round to nearest tenth)

The radius of the circle required to inscribe an equilateral triangle with the given dimensions is; radius = 3.5 inches

Usually, when we inscribe an equilateral triangle in a circle, the distance from the centroid of that triangle to one of the vertices is;

Centroid distance to vertex = ²/₃h

Where h is the altitude of the triangle.

We are given altitude = 5.196 in

Thus;

Centroid distance to vertex = ²/₃(5.196)

⇒ 3.464 inches

Approximating to the nearest tenth gives;

Centroid distance to vertex = 3.5 inches

Now, the distance from centroid to vertex of the inscribed equilateral triangle is also the radius of the circle.

Thus; radius = 3.5 inches

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Area of triangle = 1/2 base x height

15.588 = 1/2 * base x 5.196

15.588 = base x 2.598

base = 15.588 / 2.598 = 6

 equi center of triangle = 1/3*5.196 = 1.732

radius of circle = Sqrt(1.732^2 + 3^2) =

 sqrt (2.999824 +9) =

sqrt(11.999824) = 3.464

rounded to nearest tenth = 3.5 inches

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