Area - circles, sectors and segments

  • Compare Areas
    problem
    Favourite

    Compare Areas

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

    Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

  • Partly Circles
    problem
    Favourite

    Partly Circles

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

    What is the same and what is different about these circle questions? What connections can you make?

  • Bull's Eye
    problem

    Bull's Eye

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    What fractions of the largest circle are the two shaded regions?
  • 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?
  • Two Shapes & Printer Ink
    problem

    Two Shapes and Printer Ink

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    If I print this page which shape will require the more yellow ink?
  • Get Cross
    problem

    Get Cross

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
  • Round and Round
    problem

    Round and Round

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Prove that the shaded area of the semicircle is equal to the area of the inner circle.
  • Floored
    problem

    Floored

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
  • Squaring the circle
    problem

    Squaring the Circle

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.
  • Bound To Be
    problem

    Bound to Be

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Four quadrants are drawn centred at the vertices of a square . Find the area of the central region bounded by the four arcs.