Every convex body 
in the Euclidean plane
with area 
can be inscribed in a triangle of area at most equal
to 
(Gross 1918, Eggleston 1957). The worst possible fit corresponds (exclusively) to
the case that 
is a parallelogram.
Triangle Circumscribing
See also
Tetrahedron CircumscribingExplore with Wolfram|Alpha
References
Bonnesen, T. and Fenchel, W. Theory of Convex Bodies. BCS Associates, pp. 81-93, 1987.Eggleston, H. G. Problems in Euclidean Space: Applications of Convexity. New York: Pergamon, pp. 149-160, 1957.Fejes-Tóth, L. "Eine Bemerkung zur Approximation durch
-Eckringe."
Compositio Math. 7, 474-476, 1940.Finch, S. R. "Geometric
Probability Constants." §8.1 in Mathematical
Constants. Cambridge, England: Cambridge University Press, pp. 479-484,
2003.Gross, W. "Über affine Geometrie XIII: Eine Minimumeigenschaft
der Ellipse und des Ellipsoids." Berichte über die Verhandlungen der
Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Math.-Phys.
Kl. 70, 38-54, 1918.Hodges, J. L. "An Extremal
Problem of Geometry." J. London Math. Soc. 26, 311-312, 1951.Referenced on Wolfram|Alpha
Triangle CircumscribingCite this as:
Weisstein, Eric W. "Triangle Circumscribing." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriangleCircumscribing.html