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Siyavula textbooks: grade 10
Geometry basics
Polygons
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
Table of some polygons and their number of sides.
Examples of other polygons.
Angles of regular polygons
You can calculate the size of the interior angle of a regular polygon by using:
A
^
=
n
-
2
n
×
180
∘
where
n is the number of sides and
A
^ is any angle.
Areas of polygons
Area of triangle:
1
2
× base
× perpendicular height
Area of trapezium:
1
2
× (sum of
∥ (parallel) sides)
× perpendicular height
Area of parallelogram and rhombus: base
× perpendicular height
Area of rectangle: length
× breadth
Area of square: length of side
× length of side
Area of circle:
π x radius
2
Khan academy video on area and perimeter
Khan academy video on area of a circle
Polygons
For each case below, say whether the statement is true or false. For false statements, give a counter-example to prove it:
All squares are rectangles
All rectangles are squares
All pentagons are similar
All equilateral triangles are similar
All pentagons are congruent
All equilateral triangles are congruent
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
Find all the pairs of parallel lines in the following figures, giving reasons in each case.
Find angles
a ,
b ,
c and
d in each case, giving reasons.
Which of the following claims are true? Give a counter-example for those that are incorrect.
All equilateral triangles are similar.
All regular quadrilaterals are similar.
In any
▵
A
B
C
with
∠
A
B
C
=
90
∘ we have
A
B
3
+
B
C
3
=
C
A
3 .
All right-angled isosceles triangles with perimeter 10 cm are congruent.
All rectangles with the same area are similar.
Say which of the following pairs of triangles are congruent with reasons.
For each pair of figures state whether they are similar or not. Give reasons.
Challenge problem
Using the figure below, show that the sum of the three angles in a triangle is 180
∘ . Line
D
E
is parallel to
B
C .
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:
OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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