# Lesson Notes By Weeks and Term - Junior Secondary School 2

POLYGONS

TERM: 2nd TERM

SUBJECT: BASIC TECHNOLOGY

CLASS:  JSS 2

REFERENCE MATERIALS

1. MELROSE, Basic Science and Technology, Book 2
2. NERDC, Basic Technology for JSS, Book 2

WEEK THREE

TOPIC: POLYGONS

CONTENT

• Definition
• Types of polygon
• Construction of different polygons

What is a polygon?

A polygon is a plane figure with five or more straight sides. A polygon can either be regular or irregular A polygon is said to be regular it all its sides are equal and its angles are equal. An irregular polygon has unequal sides.

Types of polygons

1. Pentagon: A pentagon is a polygon with five sides.
2. Hexagon: A hexagon is a polygon with six sides
3. Heptagon: A heptagon is a polygon with seven sides.
4. Octagon: An octagon is a polygon with eight sides.
5. Nonagon: A nonagon is a polygon with nine sides.
6. Decagon: A decagon is a polygon with ten sides.

EVALUATION

1. What is a polygon?
2. Explain different types of polygon.

CONSTRUCTION OF POLYGONS

Construction of a regular Hexagon given its side.

1. Using 60o set - square

Procedure

(i)    Draw a horizontal line and mark off AB equal to the side of the hexagon.

(ii)    Through A, draw a line at 60o and mark off AC equal to AB

(iii)    Through B, draw a line at 60o and mark off BD equal to AB.

(iv)    Through C, draw a line at 60o parallel to BD and mark off CE equal to AB.

(v)    Through D, draw a line at 60o parallel to AC and mark off DF equal to AB.

(vi)    Join EF to complete the hexagon.

Using compasses: - This method is called constant radius rule.

Procedure

1. Draw a circle whose radius is equal to the side of the hexagon. Draw the horizontal diameter AB.
2. With center A and the same radius, cut the circle above AB at C and below AB at D
3. With center B and the same radius, cut the circle above AB at E and below AB at F.
4. Join AD, DF, FB, BE, EC and CA to obtain the hexagon.

Constructing a regular hexagon given the distance across flats.

Procedure

(i)    Draw a circle whose diameter is equal to the distance across flats. Draw the vertical diameter AB.

(ii)    Draw diameter CD and EF at 30o.

(iii)    Through A and B, draw horizontal tangents.

(iv)    Through C, D, E, F, in turn, draw tangents at 60o. The figure that is formed by the intersection of the tangents is the required hexagon.

This is the procedure when describing a regular hexagon about a given circle.

#### To construct a regular Octagon given its sides

Procedure

(i)    Draw a horizontal line mark off AB equal to the given side.

(ii)    Through A and B, draw lines at 45o and mark off AC and BD equal to AB.

(iii)    Through C and D, draw vertical lines and mark off CE and DF equal to AB.

(iv)    Through E and F, draw lines at 45o and mark off EG and FH equal to AB.

(v)    Join GH to complete the octagon.

To construct a rectangular octagon given the distance across flats.

Procedure

(i)    Draw a circle whose diameter is equal to the distance across flats. Draw a horizontal diameter AB and a vertical diameter CD.

(ii)    Draw diameters EF and GH at 45o

(iii)    Draw vertical tangents through A and B and horizontal tangents through C and D.

(iv)    Through E, F, G, H, in turn draw tangents at 45o. the figure formed by the intersection of the tangents is the required octagon. This is the procedure when describing a regular octagon about a given circle.

General methods for constructing a regular polygon on a given base.

1. The External Rule – 360o

Procedure

(i)    Obtain the external angle of the required polygon by dividing 360o by the number of side (N) of the polygon, i.e. external angle = 360o/N

(ii)    Draw a horizontal line and mark off AB equal to the given base.

(iii)    Through A, draw a line at 360o/N and mark off a length equal to AB. Also at B, draw a line at 360o/ N and mark off a length equal to AB.

(iv)    Continue the process until you have obtained the polygon of N sides where N = 5, 6, 7, 8, 9, 10…… Suppose that at N = 5, then external angle = 360o/5= 72o

THE TWO–TRIANGLE RULE.

Procedure

(i)    Draw a horizontal line and mark off AB equal to the given base.

(ii)    Bisect AB and produce its bisector as long as it is convenient.

(iii)    On AB as base, draw an isosceles triangle with base angle 45o and an equilateral triangle so that the apexes of the two triangles lie on the bisector of AB. Denote the apex of the isosceles triangle as F.

(iv)    Bisect FD to obtain point e.

(v)    Along the bisector of AB, from point f, step off length de (or if) to obtain points G, H, L, J, e.t.c. The points D, E, F, G, H, L, J, are the centers of the circumscribing circles for a square, regular pentagon, hexagon and decagon respectively.

(vi)    Suppose you want to draw a polygon of 8 sides (octagon).

With center h and radius HA (or HB) draw a circle. Take length AB and step it off on the circle to obtain the points C, D, E, F, G, H, I. Join the points to obtain the required regular nonagon. Note that D = 4; E = 5;F = 6;G = 7;H = 8;L = 9;J = 10

Conclusion

A polygon may be regular or irregular. When it is regular, all its sides are equal, and its angles are also equal. Polygons include pentagons, hexagons, heptagons, octagons, nonagons, and decagons, which have five, six, seven, eight, nine, and ten sides respectively.

Evaluation

1. Construct a hexagon using the 600 by 300 set-square
2. State the formula for generally constructing a polygon

REFERENCE MATERIALS

• MELROSE BASIC SCIENCE AND TECHNOLOGY BOOK 2, page 86-89
• NERDC- BASIC TECHNOLOGY BOOK 2, page 61-66

WEEKEND ASSIGNMENT

1. Which of the following is not a polygon? A. Circle B. Triangle C. Decagon D. Heptagon.
2. Two angular points are joined by a _______ A. diagonal B. vertex C. horizon D. pinnacle
3. A polygon is a plane figure with _____or more straight sides. A. Five B. three C. four D. two
4. A regular polygon has __________ of its sides and angles equal A. five B. all C. three D. four
5. An Octagon is a polygon with _________ sides A. 5 B. 6 C. 7 D. 8

THEORY

1. Define polygon
2. What are regular polygons?
3. Construct (i) a square of side 60mm (ii) a regular hexagon of side 80mm.