geometry
Power scaling of length, area, and volume — AMC & AIME Problems
34 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Power scaling of length, area, and volume — 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: Area and Perimeter of Similar Figures, Congruent and Similar Solids.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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AMC 8
AMC 10
AMC 12
- 1950 AMC 12 Problem 8
- 1950 AMC 12 Problem 33
- 1951 AMC 12 Problem 10
- 1959 AMC 12 Problem 1
- 1960 AMC 12 Problem 7
- 1960 AMC 12 Problem 21
- 1962 AMC 12 Problem 16
- 1973 AMC 12 Problem 8
- 1983 AMC 12 Problem 24
- 2004 AMC 12A Problem 9
- 2008 AMC 12B Problem 11
- 2010 AMC 12A Problem 7
- 2016 AMC 12B Problem 8
- 2016 AMC 12B Problem 23
- 2018 AMC 12A Problem 8
- 2021 AMC 12A Spring Problem 10
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
- 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