develop formulas
for the areas of
triangles and
quadrilaterals , and
apply them;
Suggested teaching activities
Ask learners to take a piece of A4 paper and
fold it diagonally, corner-to-corner.
Tell learners
that you want to know the length of the diagonal.
Agree that the diagonal creates right-angled
triangles (right triangles).
Learners might
remember that if the short side of the paper is 1
unit, the long side is √2 units long.
prove and apply
Pythagoras’
theorem;
Check if anyone has heard of, or can remember,
Pythagoras’ theorem.
Recall that it establishes a
relationship between the length of sides in a
right angled triangle, often remembered as
‘the square on the hypotenuse is equal to the
sum of the squares of the other two sides’
so in the case of the paper,
1
2 + (√2)2 = (diagonal)2
so the diagonal is √3 units long
Remember that √3 is a surd, but an
approximation is 1.732.
Learners to check by using the short side of a
paper as 1 unit, so the diagonal should be
approximately 1¾ units long – how will they test
this?
Demonstrate the classic proof of Pythagoras by
dissecting a square of side a+b , with c being the
diagonal of the rectangles a x b
There are interesting sets of integers which fulfil
the formula, the most famous being 3,4,5
However there are many more.
Learners to research Pythagorean Triples in
library or via the internet
Non-integer relationships are more difficult to
calculate, which is where trigonometry comes in.