Heron’s Formula — AMC & AIME Practice Problems | LIVE by Po-Shen Loh

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Heron’s Formula — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Heron’s Formula — a geometry concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 12

2000 AMC 12 Problem 19 · 2002 AMC 12A Problem 23 · 2008 AMC 12B Problem 18 · 2011 AMC 12B Problem 20 · 2012 AMC 12A Problem 18 · 2012 AMC 12B Problem 20 · 2024 AMC 12A Problem 24

AIME

1999 AIME Problem 12 · 2000 AIME II Problem 12 · 2003 AIME II Problem 6 · 2005 AIME I Problem 15 · 2006 AIME II Problem 15 · 2007 AIME II Problem 15 · 2009 AIME I Problem 12 · 2011 AIME I Problem 8 · 2013 AIME I Problem 13 · 2015 AIME II Problem 7 · 2024 AIME I Problem 14 · 2026 AIME II Problem 8

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3D geometry altitude angle bisector angle bisector theorem angle chasing angle sum annulus arc area area decomposition area ratio Brahmagupta’s Formula centroid chord circle circle area circumcircle, circumcenter, and circumradius circumference cone congruence (geometry)coordinate geometry cube geometry cyclic quadrilateral cylinder diagonal distance formula ellipse equiangular polygon equilateral triangle Euler’s Polyhedron Formula homothety hyperbola incircle, incenter, and inradius inscribed angle isosceles triangle kite lattice point law of cosines law of sines mass points median (geometry)midpoint net (3D geometry)paper folding parabola parallel lines parallelogram perimeter perpendicular bisector Pick’s Theorem polyhedron power of a point power scaling of length, area, and volume Ptolemy’s Theorem pyramid Pythagorean Theorem Pythagorean Triple radical axis rectangle rectangular prism reflection (geometry)regular polygon rhombus right triangle sector shoelace formula similarity special right triangle sphere square (geometry)Stewart’s Theorem surface area tangent circles tangent line transformation trapezoid triangle area triangle inequality trigonometric identity trigonometry vector Viviani’s Theorem volume