4 November 2010
Maths
● Text : Viola Ho
How can you work
out the internal angle
sum of a polygon? Put
away your protractor. There is a
simple and effective way to do it.
W
HAT exactly is a polygon? It is more
than just a straight line. It is a shape with
straight edges. A polygon needs to have
at least three sides.
Internal
angle sum
This octagon has been divided into triangles. No lines
intersect and no line touches
the sides.
What we know:
Internal angle sum of a triangle = 180°
Internal angle sum of a square = 90° x 4 = 360°
What about the internal angle sum of a polygon
with more sides?
It can be expressed in the following way:
Sum of all internal angles of
all triangles = internal angle
sum of the octagon
Answer
An n-sided polygon is a polygon with a number
of different sides. Inside the polygon are a
number of triangles.
We can work out an n -sided polygon as follows:
Internal angle sum = 180° x (n – 2)
Let’s visualise it with an octagon (an 8-sided
polygon):
P04
Thu
Number of triangles = number of green sides
=8–2=6
Internal angle sum of a triangle = 180°
Therefore the internal angle sum of the
octagon = 180° x (8 – 2) = 1080°
Similarly, you can divide an n-sided polygon
into (n – 2) triangles using the method above
and multiply the number of triangles by 180°
to get the internal sum of the polygon.
Question
1. A vertex is the corner point of a shape. Select
a vertex on a polygon.
2. Mark the two adjacent sides in red.
3. Mark all the other sides in green.
4. Link the red vertex to other vertices, except
for the adjacent two, using straight lines.
Vocabulary
protractor (n) 量角器
edge (n) 邊
As you can see, when there are more
sides, the sum of the angle gets larger.
The more sides a polygon has, the more
it looks like a circle.
So, what is the internal angle sum of a
circle? Think about it.
vertex (n) 頂點
adjacent (adj) 鄰接的
intersect (v) 交叉
internal (adj) 內的