Area - squares and rectangles

  • Numerically Equal
    problem

    Numerically equal

    Age
    7 to 11
    Challenge level
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    Can you draw a square in which the perimeter is numerically equal to the area?

  • Rope Mat
    problem

    Rope mat

    Age
    7 to 11
    Challenge level
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    How many centimetres of rope will I need to make another mat just like the one I have here?
  • Take a square
    problem

    Take a square

    Age
    14 to 16
    Challenge level
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    Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
  • Framed
    problem

    Framed

    Age
    11 to 14
    Challenge level
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    Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.
  • Compare Areas
    problem

    Compare areas

    Age
    14 to 16
    Challenge level
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    Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
  • Wrapping Presents
    problem

    Wrapping presents

    Age
    7 to 11
    Challenge level
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    Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
  • Lawn Border
    problem

    Lawn border

    Age
    5 to 11
    Challenge level
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    If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
  • Making Boxes
    problem

    Making boxes

    Age
    7 to 11
    Challenge level
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    Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

  • Two Squared
    problem

    Two squared

    Age
    7 to 11
    Challenge level
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    What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
  • Great Squares
    problem

    Great squares

    Age
    7 to 11
    Challenge level
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    Investigate how this pattern of squares continues. You could measure lengths, areas and angles.