geometry
Trapezoid — AMC & AIME Problems
65 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Trapezoid — 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: Trapezoid Area, Similar Triangles in Trapezoids, The Midsegment of a Trapezoid.
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
AMC 10
- 2001 AMC 10 Problem 24
- 2002 AMC 10A Problem 25
- 2005 AMC 10B Problem 23
- 2006 AMC 10B Problem 24
- 2008 AMC 10A Problem 20
- 2009 AMC 10B Problem 4
- 2012 AMC 10B Problem 19
- 2014 AMC 10B Problem 21
- 2018 AMC 10A Problem 24
- 2021 AMC 10A Spring Problem 17
- 2022 AMC 10A Problem 23
- 2022 AMC 10B Problem 16
- 2025 AMC 10B Problem 6
AMC 12
- 1952 AMC 12 Problem 38
- 1957 AMC 12 Problem 49
- 1959 AMC 12 Problem 22
- 1967 AMC 12 Problem 9
- 1967 AMC 12 Problem 12
- 1968 AMC 12 Problem 35
- 1969 AMC 12 Problem 22
- 1972 AMC 12 Problem 18
- 1981 AMC 12 Problem 5
- 1984 AMC 12 Problem 8
- 1989 AMC 12 Problem 4
- 2002 AMC 12B Problem 18
- 2006 AMC 12B Problem 15
- 2008 AMC 12B Problem 25
- 2009 AMC 12B Problem 4
- 2009 AMC 12B Problem 16
- 2012 AMC 12B Problem 20
- 2013 AMC 12B Problem 20
- 2021 AMC 12A Spring Problem 17
- 2021 AMC 12B Spring Problem 11
- 2021 AMC 12B Spring Problem 17
- 2021 AMC 12A Fall Problem 21
- 2021 AMC 12A Fall Problem 24
- 2022 AMC 12A Problem 20
- 2022 AMC 12A Problem 22
- 2023 AMC 12B Problem 11
AIME
- 1987 AIME Problem 6
- 1992 AIME Problem 9
- 2000 AIME II Problem 6
- 2000 AIME II Problem 8
- 2000 AIME II Problem 11
- 2004 AIME II Problem 12
- 2008 AIME I Problem 10
- 2008 AIME II Problem 5
- 2014 AIME I Problem 13
- 2014 AIME II Problem 3
- 2015 AIME I Problem 14
- 2015 AIME II Problem 4
- 2020 AIME II Problem 2
- 2021 AIME I Problem 9
- 2022 AIME I Problem 3
- 2023 AIME II Problem 9
- 2025 AIME I Problem 6
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
- Square (geometry)
- Stewart’s Theorem
- Surface area
- Tangent circles
- Tangent line
- Transformation
- Triangle area
- Triangle inequality
- Trigonometric identity
- Trigonometry
- Vector
- Viviani’s Theorem
- Volume