2D shapes and their properties

  • LOGOSquares
    problem

    LOGOsquares

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

  • Kissing
    problem

    Kissing

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
  • Baby Circle
    problem

    Baby circle

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
  • Some(?) of the Parts
    problem

    Some(?) of the parts

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
  • Chain of Changes
    problem

    Chain of changes

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

    Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

  • Two By One
    problem

    Two by one

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    An activity making various patterns with 2 x 1 rectangular tiles.
  • Rectangles with Dominoes
    problem

    Rectangles with dominoes

    Age
    5 to 7
    Challenge level
    filled star filled star empty star
    Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
  • problem

    Four triangles puzzle

    Age
    5 to 11
    Challenge level
    filled star empty star empty star

    Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

  • Watch those Wheels
    page

    Watch those wheels

    Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
  • Lafayette
    page

    Lafayette

    What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?