I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you move the tiles around, can you make squares with different coloured edges?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
Make some loops out of regular hexagons. What rules can you discover?
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
A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...