Area - squares and rectangles

  • Expanding Pattern
    problem

    Expanding Pattern

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    How many squares are needed to continue this pattern?

  • Guillotine
    problem

    Guillotine

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

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

  • Square in a Triangle
    problem

    Square in a Triangle

    Age
    11 to 14
    Challenge level
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    Weekly Problem 33 - 2006
    A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

  • Double Cover
    problem

    Double Cover

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

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

  • Tangram Area
    problem

    Tangram Area

    Age
    11 to 14
    Challenge level
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    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?

  • Framed
    problem

    Framed

    Age
    11 to 14
    Challenge level
    filled star filled star filled star

    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.

  • Four or Five
    problem

    Four or Five

    Age
    11 to 14
    Challenge level
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    The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

  • Triangle in a Hexagon
    problem

    Triangle in a Hexagon

    Age
    11 to 14
    Challenge level
    filled star filled star filled star

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

  • 11x11 square
    problem

    11×11 Square

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    Here's a neat trick you can do with an 11 by 11 square...

  • Semicircle Stack
    problem

    Semicircle Stack

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    What is the total area enclosed by the three semicicles?