Area - circles, sectors and segments

problem
Favourite

Spokes

Age

16 to 18

Challenge level

3 out of 3

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
problem

Bull's Eye

Age

11 to 14

Challenge level

1 out of 3

What fractions of the largest circle are the two shaded regions?
problem

Get Cross

Age

14 to 16

Challenge level

2 out of 3

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?
problem

Floored

Age

14 to 16

Challenge level

2 out of 3

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?
problem

Squaring the Circle

Age

11 to 14

Challenge level

2 out of 3

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.
problem

Circular Area

Age

7 to 11

Challenge level

1 out of 3

How could you find out the area of a circle? Take a look at these ways.
problem

Handy Angles

Age

11 to 14

Challenge level

2 out of 3

Weekly Problem 39 - 2008
How big is the angle between the hour hand and the minute hand of a clock at twenty to five?
problem

Square Pegs

Age

11 to 14

Challenge level

3 out of 3

Which is a better fit, a square peg in a round hole or a round peg in a square hole?
problem

Semicircle Stack

Age

14 to 16

Challenge level

1 out of 3

What is the total area enclosed by the three semicicles?
problem

Two Shapes and Printer Ink

Age

14 to 16

Challenge level

1 out of 3

If I print this page which shape will require the more yellow ink?