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?
This activity investigates how you might make squares and pentominoes from Polydron.
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. . . .
Can you find rectangles where the value of the area is the same as the value of the perimeter?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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.
I cut this square into two different shapes. What can you say about
the relationship between them?
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
Can you predict, without drawing, what the perimeter of the next
shape in this pattern will be if we continue drawing them in the
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?
Create some shapes by combining two or more rectangles. What can
you say about the areas and perimeters of the shapes you can make?