Area - circles, sectors and segments

  • Bull's Eye
    problem

    Bull's eye

    Age
    11 to 14
    Challenge level
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    What fractions of the largest circle are the two shaded regions?
  • Semicircle Stack
    problem

    Semicircle stack

    Age
    14 to 16
    Challenge level
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    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
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    If I print this page which shape will require the more yellow ink?
  • Mean Geometrically
    problem

    Mean geometrically

    Age
    16 to 18
    Challenge level
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    A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?
  • Quadarc
    problem

    Quadarc

    Age
    14 to 16
    Challenge level
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    Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.
  • Get Cross
    problem

    Get cross

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