Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Angles, Polygons and Geometrical Proof Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
  Sheet 4 Solutions
     
Stage 3 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
     
Stage 4 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
     
Stage 4 ★★★ Sheet 1 Solutions

Circled Square

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Can you find the area of this square inside a circle?

Folded Square

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

This square piece of paper has been folded and creased. Where does the crease meet the side AD?

Cut-up Square

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Weekly Problem 15 - 2015
In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?

Triangular Intersection

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

What is the largest number of intersection points that a triangle and a quadrilateral can have?

Height and Sides

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Can you find the area of the triangle from its height and two sides?

first previous 0 1
  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo