1. Polygon Constructions
Regular Pentagon and Regular Hexagon
Year 9
Mathematics

2. Pentagon Calculations.
To construct any polygon, you need to make 3 important calculations
a) Total angle sum
b) Interior angle - for a given side length (difficult).
c) Angle at the centre - construction in a circle (easy).
(1) Total angle sum.
Use the total angle sum of a polygon formula.
Angle sum = (n – 2) x 180°, where n = number of sides. i.e. n = 5.
Total angle sum = (5 – 2) x 180
= 540
(2) Interior Angle = Angle sum ÷ number of sides
= 540 ÷ 5
= 108
(3) Angle at the centre = 360 ÷ number of sides.
= 360 ÷ 5
= 72

3. Pentagon Side Construction
To construct a pentagon with a given side length, you need the interior angle, 108°and the actual side length.
Task, construct a pentagon with side length 5 cm.
Now, join the two ends.
Repeat steps (1) and (2).
(1 )Place Protractor, at the other end and measure 108°, and mark. Remove the protractor.
(2) Construct the 5 cm line.
(1) Place Protractor, at one end and measure 108°, and mark. Remove the protractor.
(2) Construct the 5cm line.
Start with a 5 cm line.

4. Construct a Pentagon in a Circle.
To construct a pentagon in a circle, you need the angle at the centre, 72°and the actual circle with the given radius.
Task, construct a pentagon in a circle of radius, r = 5 cm.
Place the protractor on the centre and radius.
Mark the 72°.
Then mark 72° + 72° = 144
Construct circle and draw in the radius.
Remove Protractor.
Draw line from the centre outwards to cut the circle.
Join the point at which each lines cuts the circle, including the radius.
Rotate protractor, and mark the 72° and 144° marks.
Remove Protractor.
Draw line from the centre outwards to cut the circle.

5. Hexagon Calculations.
To construct any polygon, you need to make 3 important calculations
a) Total angle sum
b) Interior angle - for a given side length (difficult).
c) Angle at the centre - construction in a circle (easy).
(1) Total angle sum.
Use the total angle sum formula for a polygon.
Angle sum = (n – 2) x 180° , where n = number of sides, n = 6.
Total angle sum = (6 – 2) x 180
= 720
(2) Interior Angle = Angle sum ÷ number of sides
= 720 ÷ 6
= 120
(3) Angle at the centre = 360 ÷ number of sides.
= 360 ÷ 6
= 60

6. Hexagon Side Construction
To construct a pentagon with a given side length, you need the interior angle, 108°and the actual side length.
Task, construct a Hexagon with side length 4 cm.
Now, join the two ends.
(1 )Place Protractor, at the other end and measure 120°, and mark. Remove the protractor.
(1 )Place Protractor, at the other end and measure 120°, and mark. Remove the protractor.
(2) Construct the 4 cm line.
(2) Construct the 4 cm line.
(1 )Place Protractor, at the other end and measure 120°, and mark. Remove the protractor.
(1) Place Protractor, at one end and measure 120°, and mark. Remove the protractor.
(2) Construct the 4cm line.
(2) Construct the 4 cm line.
Start with a 4 cm line.

7. Construct a Hexagon in a Circle.
To construct a hexagon in a circle, you need the angle at the centre, 60°and the actual circle with the given radius.
Task, construct a hexagon in a circle of radius, r = 5 cm.
Construct circle and draw in the radius.
Place the protractor on the centre and radius.
Mark the 60°.
Then mark 60° + 60° = 120°
Remove Protractor.
Draw lines from the centre outwards through the marks to cut the circle.
Join the point at which each lines cuts the circle, including the radius cut.
Rotate protractor, and mark the 60°, 120° and 180° marks.

8. THE END OF CONSTRUCTION.