Shoelace formula — AMC & AIME Problems | LIVE by Po-Shen Loh

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Shoelace formula — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Shoelace 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 problems are used with official legal permission of the Mathematical Association of America (MAA).

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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.

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AMC 10

2007 AMC 10A Problem 18 • 2024 AMC 10B Problem 10

AMC 12

1962 AMC 12 Problem 37 • 1985 AMC 12 Problem 13 • 2011 AMC 12A Problem 17 • 2013 AMC 12A Problem 13 • 2016 AMC 12A Problem 15 • 2017 AMC 12B Problem 24 • 2018 AMC 12A Problem 22 • 2019 AMC 12A Problem 5 • 2020 AMC 12A Problem 17 • 2021 AMC 12B Spring Problem 15 • 2021 AMC 12A Fall Problem 21 • 2022 AMC 12B Problem 25 • 2024 AMC 12B Problem 12 • 2024 AMC 12B Problem 15

AIME

1998 AIME Problem 11 • 2005 AIME I Problem 10 • 2009 AIME I Problem 11 • 2017 AIME II Problem 10 • 2022 AIME II Problem 11 • 2025 AIME I Problem 2 • 2026 AIME I Problem 10 • 2026 AIME II Problem 3

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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 British Flag Theorem centroid Ceva’s Theorem 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 Heron’s 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 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