Perimeter, Area and Volume Short Problems: Age 11-14

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Perimeter, Area and Volume: 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: Age 11-14 ⭐⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in turquoise pots.
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    Hexa-Split

    Age
    11 to 14
    Challenge level

    Which of the areas shown in the hexagons are equal to each other?

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    3×3 Areas

    Age
    11 to 14
    Challenge level

    Which of the following shaded regions has an area different from the other shaded regions?

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    Mid-Point Area

    Age
    11 to 14
    Challenge level

    M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

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    Six Circles

    Age
    11 to 14
    Challenge level

    In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?

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    Squares in a Square

    Age
    11 to 14
    Challenge level

    In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

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    Chequered Cuboid

    Age
    11 to 14
    Challenge level

    A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?

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    Star in a Hexagon

    Age
    11 to 14
    Challenge level

    Weekly Problem 20 - 2017
    The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

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    Cuboid Faces

    Age
    11 to 14
    Challenge level

    Can you find the volume of a cuboid, given the areas of its faces?

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    Giant Rubik's Cube

    Age
    11 to 14
    Challenge level

    How many cubes would be visible in a 12 by 12 by 12 Rubik's cube?

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    Nested Squares

    Age
    11 to 14
    Challenge level

    What proportion of the diagram is shaded?

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    Guillotine

    Age
    11 to 14
    Challenge level

    Weekly Problem 9 - 2006
    What fraction of the area of the rectangle is shaded?

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    L-Emental

    Age
    11 to 14
    Challenge level

    Weekly Problem 28 - 2006
    What can you say about the rectangles that form this L-shape?

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    Double Cover

    Age
    11 to 14
    Challenge level

    Weekly Problem 3 - 2007
    What is the ratio of the area of the table covered twice, to the uncovered area?

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    Exactly Three-Quarters

    Age
    11 to 14
    Challenge level

    Weekly Problem 30 - 2007
    Three-quarters of the area of the rectangle has been shaded. What is the length of x?

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    Margins

    Age
    11 to 14
    Challenge level

    Weekly Problem 16 - 2008
    A 30cm x 40cm page of a book includes a 2cm margin on each side... What percentage of the page is occupied by the margins?

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    Tangram Area

    Age
    11 to 14
    Challenge level

    Weekly Problem 29 - 2008
    The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?

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    Triangles' Triangle

    Age
    11 to 14
    Challenge level

    Weekly Problem 27 - 2009
    The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?

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    Intersecting Squares

    Age
    11 to 14
    Challenge level

    Weekly Problem 32 - 2014
    Three overlapping squares are shown. If you know the areas of the overlapping and non-overlapping parts, can you work out the side lengths of the squares?

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    Sideways Ratio

    Age
    11 to 14
    Challenge level

    Weekly Problem 33 - 2014
    A rectangle with area $125\text{cm}^2$ has sides in the ratio $4:5$. What is the perimeter of the rectangle?

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    Cubic Masterpiece

    Age
    11 to 14
    Challenge level

    Weekly Problem 49 - 2014
    A blue cube is cut into 27 smaller cubes of equal size. What fraction of the total surface area of these cubes is blue?

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    Open the Box

    Age
    11 to 14
    Challenge level

    Weekly Problem 37 - 2015
    A piece of card is folded to make an open box. Given its surface area, can you work out its volume?

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    Shaded End

    Age
    11 to 14
    Challenge level

    If the area of a face of a cuboid is one quarter of the area of each of the other two visible faces, what is the area of these faces?

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    Cubes on a Cube

    Age
    11 to 14
    Challenge level

    Weekly Problem 26 - 2016
    A cube has each of its faces covered by one face of an identical cube, making a solid as shown. What is the surface area of the solid?

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    Line of Squares

    Age
    11 to 14
    Challenge level

    Weekly Problem 35 - 2016
    What is the total perimeter of the squares, if the line GH in the diagram is 24cm?

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    Strawberries and Peas

    Age
    11 to 14
    Challenge level

    Weekly Problem 17 - 2017
    Yasmin lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by $15m^2$. What was the original area of her pea bed?

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    Corner Cut

    Age
    11 to 14
    Challenge level

    Weekly Problem 23 - 2017
    Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

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    Leaning Over

    Age
    11 to 14
    Challenge level

    Weekly Problem 31 - 2017
    The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

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    Christmas Cut-Out

    Age
    11 to 14
    Challenge level

    Weekly Problem 52 - 2017
    Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?

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    Hawaiian Earring

    Age
    11 to 14
    Challenge level

    What fraction of the larger circle is outside the smaller circle?

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    Scalene Area

    Age
    11 to 14
    Challenge level

    Can you find the area of this scalene triangle?

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    Tile Border

    Age
    11 to 14
    Challenge level

    What is the largest possible number of yellow tiles in this pattern?

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    Tilted Tank

    Age
    11 to 14
    Challenge level

    Can you find the height of the water in this tilted tank when it is flat?

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    Dividing a Square

    Age
    11 to 14
    Challenge level

    A square is divided into three shapes which all have equal areas. Can you find the length of this side?

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    Semicircle Shape

    Age
    11 to 14
    Challenge level

    Find the shaded area of these shapes with perimeters made of semicircles.

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    Packing Small Boxes

    Age
    11 to 14
    Challenge level

    How many small boxes will fit inside the big box?

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    Hexagon Slices

    Age
    11 to 14
    Challenge level

    Weekly Problem 37 - 2007
    This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

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    Triangle in a Hexagon

    Age
    11 to 14
    Challenge level

    Weekly Problem 3 - 2009
    What fraction of the area of this regular hexagon is the shaded triangle?

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    Four Square

    Age
    11 to 14
    Challenge level

    Weekly Problem 17 - 2015
    A square contains two overlapping squares. What is the total of the shaded regions?

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    Pile Driver

    Age
    11 to 14
    Challenge level

    Weekly Problem 38 - 2015
    Where does the line through P that halves the figure shown meet the edge XY?

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    Rectangle Split

    Age
    11 to 14
    Challenge level

    Draw another line through the centre of this rectangle to split it into 4 pieces of equal area.

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