Area - squares and rectangles

  • Changing areas, changing perimeters
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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?

  • 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?

  • 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?

  • 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?

  • Perimeter Challenge
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    Perimeter Challenge

    Age
    11 to 14
    Challenge level

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

  • Completing Quadrilaterals
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    Completing Quadrilaterals

    Age
    11 to 14
    Challenge level

    We started drawing some quadrilaterals - can you complete them?

  • A blue patchwork quilt draped over a white sofa.
    problem
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    Alison's Quilt

    Age
    11 to 14
    Challenge level

    Nine squares are fitted together to form a rectangle. Can you find its dimensions?

  • Warmsnug Double Glazing
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    Warmsnug Double Glazing

    Age
    14 to 16
    Challenge level

    How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

  • Semi-detached
    problem
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    Semi-Detached

    Age
    14 to 16
    Challenge level

    A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

  • The square under the hypotenuse
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    The Square Under the Hypotenuse

    Age
    14 to 16
    Challenge level

    Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

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