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?
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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.
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.
Can you find rectangles where the value of the area is the same as the value of the perimeter?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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
Create some shapes by combining two or more rectangles. What can
you say about the areas and perimeters of the shapes you can make?
Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .
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?
An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Look at the mathematics that is all around us - this circular
window is a wonderful example.
Can you draw a square in which the perimeter is numerically equal
to the area?
Can you predict, without drawing, what the perimeter of the next
shape in this pattern will be if we continue drawing them in the
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Use the information on these cards to draw the shape that is being described.
I cut this square into two different shapes. What can you say about
the relationship between them?
This activity investigates how you might make squares and pentominoes from Polydron.
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
If I use 12 green tiles to represent my lawn, how many different
ways could I arrange them? How many border tiles would I need each