3.16 Polygons

Mathematics

Space and shape

Educator section

Memorandum

15.2

(a) concave

(b) concave

(c) convex

16.1

(a) rhombus

(b) trapezium

(c) octagon

(d) quadrilateral polygon

(e) hexagon

(f) heptagon

(g) pentagon

(h) parallelogram

16.2

16.3 108°

17.1 SIMILARITIES

* 4 equally long sides

sides ⁄ ⁄

* diagonals half each other

* 4 corners

DIFFERENCES

* angles of

rhombus not 90°

17.2 SIMILARITIES

* have 2 pairs of equally long sides

* 2 opposite sides are equally long

* have 4 corners

* diagonals halve (bisect) each other

DIFFERENCES

* angles of parallelogram not 90°

18.

(a) kite

(b) trapezium

20.2 ceilings; gates; trusses; bridges; scaffolding

Leaner section

Content

Activity: polygons [lo 3.1, lo 2.3]

15. POLYGONS

15.1 Did you know?

Geometric forms in a plane that are made up of straight lines are called polygons. These are made up of sides, angles or corners and vertices.

15.2 Did you also know?

A polygon is convex if all the lines that join any two vertices are inside the polygon.

All the inner angles are either acute or obtuse angles.

The polygon will be concave if any lines that join two vertices fall outside the polygon.

Then one or more of the inside angles will be a reflex angle.

15.2.1 Are the following polygons convex or concave?

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b)

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c)

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15.3 Also Remember!

The sides of a regular polygon are equally long and all the angles are equally big.

The more sides a regular polygon has, the bigger the inside angles become.

The sides of an irregular polygon are all of different lengths.

15.4 TAKE NOTE!

We can calculate the size of the angles of a regular polygon with the help of this formula:

e.g. Hexagon:

16.1 Work with a friend. Can you say what each of the following polygons are called? Write the name in each figure.

a)

b)

c)

d)

e)

f)

g)

h)

16.2 Calculate the size of each angle of the octagon.

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16.3 What is the size of each angle of a pentagon?

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17.1 Work in groups of three. Cut strips of thick cardboard or use ice cream sticks. Make holes at the ends and join the sticks with split pins. Build a square.

Press on one corner and change it into a rhombus.

• Now compare the square with the rhombus and see if you can complete the following table:

SIMILARITIES

between rhombus and square

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