Perimeter and Area
Yr 7
QCA, HBS, Ri
Pin-board shapes
Draw shapes on the pin-board by joining dots.
Write down the following information for the shape:
1. Count the dots around the perimeter (D.P.)
2. Count the dots inside the shape (D.I.)
3. Calculate the area of the shape (A.)
Pin-board shapes
Shape
A
D.I.
D.P.
No.1
1
0
4
No.2
5
1
10
No.3
5
2
8
...
...
...
...
Comments
...
At home...
Conduct your investigation and write down
any patterns relating the three variables
that you find.
Find a formula for the area of a shape
using the dots in the perimeter and
number of dots in the middle.
Give reasons for why your formula works.
Pick’s Theorem
Does the number of dots in the perimeter
give us the length of the perimeter of the
shape?
Who was Pick?
Georg Alexander Pick
August 10, 1859 – July 26, 1942
Born in Austria, died in Bohemia, now
Czech Republic
Pick’s Theorem...
… is not a relationship about perimeter and
area!
Pick’s Theorem
What did you discover?
Perimeter and area
Is there always a
relationship
between perimeter
and area?
Draw a shape with area 24,
what’s the perimeter of your
shape?
What’s the longest
perimeter you can make?
Draw a shape with
perimeter 24,
what’s the area of
your shape?
What’s the
smallest area
you can make?
Activity
Ask pupils to investigate rectangles with the
perimeter and area in the previous slide
using their maths books (squared paper)
Perimeter, area,
shapes and designing
clothes
...
Which shapes match?
?
Make your own match
In pairs, cut the sleeve of the old t-shirt.
In the body of the t-shirt draw a shape that
you can ‘sew’ the sleeve into – you
cannot chose a circle.
What is your guess of how it will look like?
If you have time repeat with the other
sleeve, with a different shape
Plan your design, draw the shape.
Cut out the shape to make a hole.
Create your design by stapling the sleeve
into your hole.
Perimeter, area, shapes
and designing clothes
Can you
explain your
design
process?
How did you know
you would be able to
sew the sleeve into
the hole?
What shape
was your
hole?