Area - squares and rectangles

  • Small pepper seedlings in orange pots.
    problem

    Expanding Pattern

    Age
    11 to 14
    Challenge level
    1 out of 3

    How many squares are needed to continue this pattern?

  • Small pepper seedlings in turquoise pots.
    problem

    Guillotine

    Age
    11 to 14
    Challenge level
    2 out of 3

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

  • Small pepper seedlings in turquoise pots.
    problem

    Square in a Triangle

    Age
    11 to 14
    Challenge level
    2 out of 3

    Weekly Problem 33 - 2006
    A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

  • Small pepper seedlings in turquoise pots.
    problem

    Double Cover

    Age
    11 to 14
    Challenge level
    2 out of 3

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

  • Small pepper seedlings in turquoise pots.
    problem

    Tangram Area

    Age
    11 to 14
    Challenge level
    2 out of 3

    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
    3 out of 3

    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.

  • Small tomato seedlings in pink pots.
    problem

    Four or Five

    Age
    11 to 14
    Challenge level
    3 out of 3

    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Triangle in a Hexagon

    Age
    11 to 14
    Challenge level
    3 out of 3

    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
    2 out of 3

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

  • Small pepper seedlings in turquoise pots.
    problem

    Semicircle Stack

    Age
    14 to 16
    Challenge level
    1 out of 3

    What is the total area enclosed by the three semicicles?