Angles, Polygons and Geometrical Proof Short Problems: Age 11-14

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.

We have put together a selection of these short problems as printable worksheets:

Printable worksheets: Age 11-14 ⭐   Printable worksheets: Age 11-14 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in turquoise pots.
    problem

    Hexagon Cut Out

    Age
    11 to 14
    Challenge level

    Weekly Problem 52 - 2012
    An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

  • Small pepper seedlings in turquoise pots.
    problem

    Parallelogram in the Middle

    Age
    11 to 14
    Challenge level

    Weekly Problem 27 - 2013
    The diagram shows a parallelogram inside a triangle. What is the value of $x$?

  • Small pepper seedlings in turquoise pots.
    problem

    Equal Lengths

    Age
    11 to 14
    Challenge level

    Weekly Problem 29 - 2013
    An equilateral triangle is drawn inside a rhombus, both with equal side lengths. What is one of the angles of the rhombus?

  • Small pepper seedlings in turquoise pots.
    problem

    Trapezium Arch

    Age
    11 to 14
    Challenge level

    Weekly Problem 27 - 2007
    Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?

  • Small pepper seedlings in turquoise pots.
    problem

    Overbearing

    Age
    11 to 14
    Challenge level

    A village has a pub, church and school. What is the bearing of the school from the church?

  • Small pepper seedlings in turquoise pots.
    problem

    Two Isosceles

    Age
    11 to 14
    Challenge level

    Weekly Problem 37 - 2017
    A quadrilateral is divided into two isosceles triangles. Can you work out the perimeter of the quadrilateral?

  • Small pepper seedlings in turquoise pots.
    problem

    Clock Face Angles

    Age
    11 to 14
    Challenge level

    The time is 20:14. What is the smaller angle between the hour hand and the minute hand on an accurate analogue clock?

  • Small pepper seedlings in turquoise pots.
    problem

    Clock Angle

    Age
    11 to 14
    Challenge level

    What is the angle between the the hands of a clock at 8:24?

  • Small pepper seedlings in turquoise pots.
    problem

    Inner Rectangle

    Age
    11 to 14
    Challenge level

    If the shape on the inside is a rectangle, what can you say about the shape on the outside?

  • Small pepper seedlings in turquoise pots.
    problem

    No Rights

    Age
    11 to 14
    Challenge level

    Prove that the angle bisectors of a triangle can never meet at right angles.

  • Small pepper seedlings in turquoise pots.
    problem

    Add All the Angles

    Age
    11 to 14
    Challenge level

    Find the sum of all of the angles denoted by letters in this diagram

Displaying 61 - 71 of 71