geometry
Square (geometry) — AMC & AIME Problems
94 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Square (geometry) — 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Properties of Squares.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
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.
AMC 8
- 1985 AMC 8 Problem 12
- 1994 AMC 8 Problem 19
- 1995 AMC 8 Problem 6
- 1995 AMC 8 Problem 18
- 1997 AMC 8 Problem 7
- 2000 AMC 8 Problem 6
- 2005 AMC 8 Problem 4
- 2005 AMC 8 Problem 25
- 2006 AMC 8 Problem 5
- 2007 AMC 8 Problem 22
- 2008 AMC 8 Problem 23
- 2010 AMC 8 Problem 16
- 2011 AMC 8 Problem 25
- 2012 AMC 8 Problem 25
- 2015 AMC 8 Problem 25
- 2018 AMC 8 Problem 22
- 2020 AMC 8 Problem 24
- 2024 AMC 8 Problem 3
- 2026 AMC 8 Problem 13
AMC 10
- 2005 AMC 10A Problem 8
- 2005 AMC 10A Problem 19
- 2005 AMC 10B Problem 7
- 2006 AMC 10A Problem 17
- 2006 AMC 10B Problem 5
- 2006 AMC 10B Problem 8
- 2007 AMC 10A Problem 15
- 2007 AMC 10B Problem 7
- 2007 AMC 10B Problem 18
- 2008 AMC 10A Problem 10
- 2010 AMC 10A Problem 2
- 2011 AMC 10A Problem 11
- 2012 AMC 10A Problem 2
- 2014 AMC 10A Problem 13
- 2014 AMC 10A Problem 18
- 2017 AMC 10A Problem 21
- 2018 AMC 10B Problem 15
- 2020 AMC 10B Problem 21
- 2021 AMC 10A Fall Problem 7
- 2021 AMC 10B Fall Problem 13
- 2021 AMC 10B Fall Problem 15
- 2021 AMC 10B Fall Problem 25
- 2022 AMC 10A Problem 5
- 2023 AMC 10A Problem 11
AMC 12
- 1951 AMC 12 Problem 3
- 1951 AMC 12 Problem 48
- 1952 AMC 12 Problem 33
- 1954 AMC 12 Problem 8
- 1959 AMC 12 Problem 31
- 1960 AMC 12 Problem 6
- 1960 AMC 12 Problem 21
- 1961 AMC 12 Problem 39
- 1963 AMC 12 Problem 10
- 1963 AMC 12 Problem 15
- 1963 AMC 12 Problem 25
- 1964 AMC 12 Problem 10
- 1966 AMC 12 Problem 4
- 1967 AMC 12 Problem 3
- 1968 AMC 12 Problem 31
- 1970 AMC 12 Problem 2
- 1970 AMC 12 Problem 7
- 1972 AMC 12 Problem 13
- 1973 AMC 12 Problem 11
- 1975 AMC 12 Problem 4
- 1975 AMC 12 Problem 23
- 1976 AMC 12 Problem 3
- 1979 AMC 12 Problem 3
- 1980 AMC 12 Problem 4
- 1981 AMC 12 Problem 2
- 1984 AMC 12 Problem 10
- 1989 AMC 12 Problem 3
- 1989 AMC 12 Problem 23
- 2003 AMC 12A Problem 14
- 2005 AMC 12A Problem 7
- 2006 AMC 12A Problem 6
- 2007 AMC 12A Problem 23
- 2007 AMC 12B Problem 7
- 2009 AMC 12A Problem 8
- 2011 AMC 12A Problem 18
- 2021 AMC 12A Fall Problem 6
- 2023 AMC 12A Problem 9
More geometry concepts
- 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
- Shoelace formula
- Similarity
- Special right triangle
- Sphere
- Stewart’s Theorem
- Surface area
- Tangent circles
- Tangent line
- Transformation
- Trapezoid
- Triangle area
- Triangle inequality
- Trigonometric identity
- Trigonometry
- Vector
- Viviani’s Theorem
- Volume