More Transformations on a Pegboard
There are 20 right-angled triangles in total:
12 made by moving the "top"vertex - the 6 below and then each one
reflected in a vertical mirror line half way along the base:
4 made by moving the "left" vertex:
And 4 made by moving the "right" vertex:
The area of a right-angled triangle of base 6 and height 3 =
½ x 6 x 3 = 9 . This is because a right-angled triangle
has thesame area as half of a rectangle with base 6 and height
3.
Other triangles with base 6 and height 3 have the same area
regardless of whether or not they are right-angled.You can
demonstrate this by dividing each of them into two right-angled
triangles and adding the areas together. For example let's look at
the original triangle in this problem:
The triangle on the left has area = ½ x 2 x 3 = 3
The triangle on the right has area = ½ x 4 x 3 = 6
Total area = 9
This always works, so it means that you can calculate the area of
any triangle in the same way that you would calculate it for
right-angled triangles, that is½ x base x height.