# 6.3 Polygons

 Page 1 / 1

## Other polygons

There are many other polygons, some of which are given in the table below.

 Sides Name 5 pentagon 6 hexagon 7 heptagon 8 octagon 10 decagon 15 pentadecagon

## Angles of regular polygons

You can calculate the size of the interior angle of a regular polygon by using:

$\stackrel{^}{A}=\frac{n-2}{n}×{180}^{\circ }$

where $n$ is the number of sides and $\stackrel{^}{A}$ is any angle.

## Areas of polygons

1. Area of triangle: $\frac{1}{2}×$ base $×$ perpendicular height
2. Area of trapezium: $\frac{1}{2}×$ (sum of $\parallel$ (parallel) sides) $×$ perpendicular height
3. Area of parallelogram and rhombus: base $×$ perpendicular height
4. Area of rectangle: length $×$ breadth
5. Area of square: length of side $×$ length of side
6. Area of circle: $\pi$ x radius ${}^{2}$

## Polygons

1. For each case below, say whether the statement is true or false. For false statements, give a counter-example to prove it:
1. All squares are rectangles
2. All rectangles are squares
3. All pentagons are similar
4. All equilateral triangles are similar
5. All pentagons are congruent
6. All equilateral triangles are congruent
2. Find the areas of each of the given figures - remember area is measured in square units (cm ${}^{2}$ , m ${}^{2}$ , mm ${}^{2}$ ).

## Summary

• Make sure you know what: quadrilaterals, vertices, sides, angles, parallel lines, perpendicular lines,diagonals, bisectors and transversals mean.
• Similarities and differences between quadrilaterals
• Properties of triangles and quadrilaterals
• Congruency of triangles
• Classification of angles into acute, right, obtuse, straight, reflex or revolution
• Theorem of Pythagoras which is used to calculate the lengths of sides of a right-angled triangle
• Angles:
• Acute angle: An angle 0 and 90
• Right angle: An angle measuring 90
• Obtuse angle: An angle 90 and 180
• Straight angle: An angle measuring 180◦
• Reflex angle: An angle 180 and 360
• Revolution: An angle measuring 360
• Angle properties and names
• Equilateral, isoceles, right-angled, scalene triangles
• Triangles angles = 180
• Congruent and similar triangles
• Pythagoras
• Trapezium, parm, rectangle, square, rhombus, kite and properties
• Areas of particular figures

## Exercises

1. Find all the pairs of parallel lines in the following figures, giving reasons in each case.
2. Find angles $a$ , $b$ , $c$ and $d$ in each case, giving reasons.
3. Which of the following claims are true? Give a counter-example for those that are incorrect.
1. All equilateral triangles are similar.
2. All regular quadrilaterals are similar.
3. In any $▵ABC$ with $\angle ABC={90}^{\circ }$ we have $A{B}^{3}+B{C}^{3}=C{A}^{3}$ .
4. All right-angled isosceles triangles with perimeter 10 cm are congruent.
5. All rectangles with the same area are similar.
4. Say which of the following pairs of triangles are congruent with reasons.
5. For each pair of figures state whether they are similar or not. Give reasons.

## Challenge problem

1. Using the figure below, show that the sum of the three angles in a triangle is 180 ${}^{\circ }$ . Line $DE$ is parallel to $BC$ .

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Got questions? Join the online conversation and get instant answers!