Geometry

Geometry is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. Expected questions involve calculating lengths, angles, areas, and volumes of various shapes, understanding geometric theorems, and solving problems related to spatial reasoning.

Solid Geometry / Geometry in Space Trigonometry Spherical Geometry Plane Geometry Vectors

• Orange Star of David

  The area of the blue triangle is equal to 1. Calculate the area of the orange Star of David:

  

  Topics:

  Geometry -> Area Calculation Geometry -> Plane Geometry -> Triangles Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 3

• Angles

  Calculate the sum of the marked angles:

  

  Topics:

  Geometry -> Plane Geometry -> Triangles Geometry -> Plane Geometry -> Angle Calculation
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 5

• More Game Cubes

  Aviv has game cubes, where two opposite faces of each are painted red and the rest are blue.
  Aviv glued together a `3 xx 3 xx 3` cube from the game cubes. Then his friend Kfir came and calculated the total red area on the surface of the large cube.
  What is the largest result Kfir can get?

  Topics:

  Geometry -> Solid Geometry / Geometry in Space Combinatorics -> Combinatorial Geometry Minimum and Maximum Problems / Optimization Problems Combinatorics -> Colorings
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 6

• How many triangles?

  How many triangles are there in the picture?

  

  Topics:

  Geometry -> Plane Geometry -> Triangles Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Geometry -> Plane Geometry -> Angle Calculation Number Theory -> Division
  Sources:
  • Bar-Ilan's weekly mathriddle competition, 2024 Question 7

• How Many Triangles - 2?

  How many triangles are in the picture?

  

  Topics:

  Geometry -> Area Calculation Geometry -> Plane Geometry -> Triangles Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 6

• 5 Lines, 8 Intersections

  Draw 5 lines such that there are exactly 8 points of intersection between them.

  Topics:

  Combinatorics -> Combinatorial Geometry Geometry -> Plane Geometry Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 1

• Dissect into four parts

  Geometric shapes are called congruent if they coincide when superimposed. Cut the following shape into four congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 3

• Blue or Orange?

  In the diagram, there is a square ABCD and a parallelogram BCEF. Which area is larger: the blue or the orange?

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 3

• Cut a Boat in Half

  Geometric shapes are called congruent if they coincide when placed on top of each other. Cut the shape into two congruent parts

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 6

• Largest Perimeter

  A polygon with an area of 12 is drawn on grid paper, with all its sides passing through the grid lines. What is the largest possible perimeter of this polygon?

  Topics:

  Geometry -> Area Calculation Minimum and Maximum Problems / Optimization Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 5