geometry
Rectangle — AMC & AIME Problems
78 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Rectangle — 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 Rectangles.
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.
AMC 8
AMC 10
- 2000 AMC 10 Problem 7
- 2003 AMC 10B Problem 20
- 2005 AMC 10A Problem 4
- 2006 AMC 10B Problem 5
- 2008 AMC 10A Problem 14
- 2009 AMC 10A Problem 14
- 2010 AMC 10A Problem 2
- 2011 AMC 10A Problem 9
- 2011 AMC 10B Problem 14
- 2011 AMC 10B Problem 18
- 2012 AMC 10A Problem 2
- 2012 AMC 10B Problem 2
- 2014 AMC 10A Problem 16
- 2014 AMC 10B Problem 15
- 2015 AMC 10A Problem 11
- 2016 AMC 10A Problem 19
- 2016 AMC 10B Problem 19
- 2017 AMC 10A Problem 3
- 2018 AMC 10B Problem 1
- 2021 AMC 10A Spring Problem 24
- 2021 AMC 10A Fall Problem 2
- 2022 AMC 10A Problem 10
- 2023 AMC 10A Problem 17
- 2023 AMC 10B Problem 4
- 2024 AMC 10A Problem 16
AMC 12
- 1950 AMC 12 Problem 47
- 1951 AMC 12 Problem 2
- 1952 AMC 12 Problem 39
- 1952 AMC 12 Problem 46
- 1953 AMC 12 Problem 32
- 1953 AMC 12 Problem 46
- 1955 AMC 12 Problem 14
- 1957 AMC 12 Problem 37
- 1958 AMC 12 Problem 47
- 1960 AMC 12 Problem 37
- 1962 AMC 12 Problem 16
- 1963 AMC 12 Problem 32
- 1964 AMC 12 Problem 33
- 1966 AMC 12 Problem 14
- 1967 AMC 12 Problem 11
- 1967 AMC 12 Problem 19
- 1968 AMC 12 Problem 24
- 1970 AMC 12 Problem 12
- 1972 AMC 12 Problem 26
- 1977 AMC 12 Problem 26
- 1979 AMC 12 Problem 1
- 1984 AMC 12 Problem 4
- 1985 AMC 12 Problem 17
- 1989 AMC 12 Problem 3
- 1989 AMC 12 Problem 5
- 2005 AMC 12A Problem 3
- 2010 AMC 12B Problem 2
- 2012 AMC 12B Problem 2
- 2014 AMC 12B Problem 5
- 2016 AMC 12B Problem 9
- 2016 AMC 12B Problem 10
- 2021 AMC 12A Fall Problem 2
- 2022 AMC 12A Problem 3
More geometry concepts
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- 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
- 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