Perimeter, Area and Volume: Age 11-14

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.


  • Blue and White
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    Favourite

    Blue and White

    Age
    11 to 14
    Challenge level

    Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

  • Fence it
    problem
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    Fence It

    Age
    11 to 14
    Challenge level

    If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

  • Isosceles Triangles
    problem
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    Isosceles Triangles

    Age
    11 to 14
    Challenge level

    Draw some isosceles triangles with an area of $9cm^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

  • Two white rectangles on a wooden background, arranged like an equals sign.
    problem
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    Can They Be Equal?

    Age
    11 to 14
    Challenge level

    Can you find rectangles where the value of the area is the same as the value of the perimeter?

  • Changing areas, changing perimeters
    problem
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    Changing Areas, Changing Perimeters

    Age
    11 to 14
    Challenge level

    How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

  • Perimeter Possibilities
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    Perimeter Possibilities

    Age
    11 to 14
    Challenge level

    I'm thinking of a rectangle with an area of 24. What could its perimeter be?

  • Triangles in a Square
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    Triangles in a Square

    Age
    11 to 14
    Challenge level

    What are the possible areas of triangles drawn in a square?

  • Perimeter Challenge
    problem
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    Perimeter Challenge

    Age
    11 to 14
    Challenge level

    Can you deduce the perimeters of the shapes from the information given?

  • Colourful Cube
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    Colourful Cube

    Age
    11 to 14
    Challenge level

    A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

  • Isometric Areas
    problem
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    Isometric Areas

    Age
    11 to 14
    Challenge level

    We usually use squares to measure area, but what if we use triangles instead?

  • An Unusual Shape
    problem
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    An Unusual Shape

    Age
    11 to 14
    Challenge level

    Can you maximise the area available to a grazing goat?

  • Shear Magic
    problem
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    Shear Magic

    Age
    11 to 14
    Challenge level

    Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

  • On the Edge
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    On the Edge

    Age
    11 to 14
    Challenge level

    If you move the tiles around, can you make squares with different coloured edges?

  • Sending a Parcel
    problem
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    Sending a Parcel

    Age
    11 to 14
    Challenge level

    What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

  • Changing areas, changing volumes
    problem
    Favourite

    Changing Areas, Changing Volumes

    Age
    11 to 14
    Challenge level

    How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

  • More Isometric Areas
    problem
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    More Isometric Areas

    Age
    11 to 14
    Challenge level

    Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

  • Cuboids
    problem
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    Cuboids

    Age
    11 to 14
    Challenge level

    Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

  • Efficient cutting
    problem
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    Efficient Cutting

    Age
    11 to 14
    Challenge level

    Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

  • Cola can
    problem
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    Cola Can

    Age
    11 to 14
    Challenge level

    An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

  • Cuboid challenge
    problem
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    Cuboid Challenge

    Age
    11 to 16
    Challenge level

    What's the largest volume of box you can make from a square of paper?

  • Triangle in a Trapezium
    problem
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    Triangle in a Trapezium

    Age
    11 to 16
    Challenge level

    Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

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