Area - circles, sectors and segments

problem
Handy angles

Age

11 to 14

Challenge level

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
Two circles

Age

14 to 16

Challenge level

Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?
problem
Square pegs

Age

11 to 14

Challenge level

Which is a better fit, a square peg in a round hole or a round peg in a square hole?
problem
The pillar of Chios

Age

14 to 16

Challenge level

Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
problem
Approximating pi

Age

14 to 18

Challenge level

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
problem
Crescents and triangles

Age

14 to 16

Challenge level

Can you find a relationship between the area of the crescents and the area of the triangle?
problem
Running race

Age

14 to 16

Challenge level

Weekly Problem 13 - 2006
If three runners run at the same constant speed around the race tracks, in which order do they finish?
problem
Spokes

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

Can you work out the shaded area surrounded by these arcs?
problem
Circular area

Age

7 to 11

Challenge level

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