2D shapes and their properties

Investigate these hexagons drawn from different sized equilateral triangles.

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

Weekly Problem 45 - 2008
The diagram shows a regular pentagon with two of its diagonals. If all the diagonals are drawn in, into how many areas will the pentagon be divided?

These four touching circles have another circle hiding amongst them...

'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?

Which of these quadrilaterals can you find in the hexagon?

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

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.