Area

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Area Volume

• Learning Outcomes
• Find the area of square, rectangles, triangles,
  parallelograms, rhombuses, kites, trapezia and
  shapes which are composites of these.
• Find the circumference and area of a circle, to
  include inverse calculations.
• Find the area and circumference of a sector and
  segment of a circle.
• Find the surface areas and volumes of prisms.
• Find the surface area and volume of the cylinder
  to include inverse calculations
• Find the surface area and volumes of the cone and
  sphere to include inverse calculations.
• Find the surface areas and volumes of compound
  shapes most of which are everyday objects.
• Distinguish between formulae for perimeter, area
  and volume by considering dimensions.

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Area Volume
Area of Shapes
Triangles Area ½ base perp. height A ½ b
h
A ½ ab sin C
Area ½ product of 2 sides sine
of angle between them
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Area Volume
Area of Shapes
Trapezium One pair of parallel sides
Total area bh ½.ah - ½.bh ½.bh ½.ah
h/2(ab)
Area 1 ? b h
Area 2 ? ½ (a b) h
Area of a trapezium ½ (a b) h
h/2(ab)
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Area Volume
Area of Shapes
Parallelogram
Kite
Area a b length perp. height
Area ½ ab ½ length width
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Area Volume
Area of Shapes
Find the area of the following shapes
1.
2.
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Area Volume
Area and Perimeter
Circles
C
AB diameter of circle
OC radius of circle
B
A
O
DE chord of circle
E
D
Area of a circle A p r2
Perimeter of a circleCircumference C p d
C 2 p r
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Area Volume
Area and Perimeter
Find the area and perimeter of
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Area Volume
Area and Perimeter
1. The area of a circle is 51.6cm2. Calculate
its radius.
2. The circumference of a circle is 50cm.
Calculate its area.
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Area Volume
Area and Perimeter
3. The radius of a car wheel is 53cm. How many
revolutions does the wheel make in travelling
50m?
?
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Area Volume
Area and Perimeter
4. Find the shaded area.
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Area Volume
Sectors of a Circle Area and Perimeter
Consider a sector of a circle which subtends an
angle of 60 at the centre.

• Find
• The area of this sector
• The arc length AB
• The perimeter of the shape OAB

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Area Volume
Sectors of a Circle Area and Perimeter
In general
?
r
Arc length ? 2 p r 360
Area ? p r2 360
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Area Volume
Sectors, Segments, Chords and Area
OA radius AB chord
The chord AB subtends an angle of 150 at the
centre of the circle. The radius of the circle
is 7cm.
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Area Volume
Trigonometry
sin x opposite . hypotenuse
Remember SOH CAH TOA
cos x adjacent . hypotenuse
tan x opposite adjacent
1.
2.
3.
40
15
x
8
x
x
3
30
40
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Area Volume
Volume of Prism
Volume of a prism cross sectional area length
Cylinder
V p r2 h
Complete the table below (cylinders)
r h V



4
3
a)
5
128
b)
3.2
125
c)
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Area Volume
Volume of Prism
Volume of a prism cross sectional area length
Trapezoidal
V ½ (a b)h l
Example
Cross-sectional area
Volume V
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Area Volume
Volume of Prism
Cone
Pyramid
Sphere
a, b dimensions of base h perpendicular
height
r radius h perpendicular height l slant
length
r radius
V 4/3 p r3
V 1/3 base area height
V 1/3 p r2 h
Find the volume of (i) Pyramid (ii)
Cone (iii) Sphere a 3, b 4, h 2
r 2, h 4.5 r 1.5
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Area Volume
Volume of Prism
Find r.
r
V 250cm3
Find h.
Find r.
6
r
V 300cm3
V 210cm3
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Surface Area of a Cone, Sphere Cylinder
Area Volume
Sphere
Cone
SA p rl
SA 4 p r2
cylinder
SA Curved surface area Top Bottom
Curved area
2 p rh
SA 2 p rh 2 p r2
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Surface Area of a Cone, Sphere Cylinder
Area Volume
Calculate the Surface Area of
a)
d)
5
3
e)
b)
l
14.8
6
4
6
c)
5.2
r 1.8
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Area Volume
SOH CAH TOA
Use Trig to find angle marked x in the following
triangles
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Area Volume
Using Trig in Area Calculations

• Find
• The angle AOB
• The area of sector AOB
• Area of triangle AOB
• The shaded area

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Area Volume
Dimensions
Distinguishing between length, area volume
Formulae can be used to calculate length e.g.
b
Volume V p r2 h
PerimeterP 2a 2b
a
L2 L2 L3 (Volume)
L L L (Length)
Area A a b
L L L2 (Area)
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Area Volume
Dimensions
Further Examples
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Area Volume
Additional Notes
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Area Volume
Learning Outcomes At the end of the topic I will
be able to
Can Revise Do Further

• Find the area of square, rectangles, triangles,
  parallelograms, rhombuses, kites, trapezia and
  shapes which are composites of these.
• Find the circumference and area of a circle, to
  include inverse calculations.
• Find the area and circumference of a sector and
  segment of a circle.
• Find the surface areas and volumes of prisms.

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• Find the surface area and volume of the cylinder
  to include inverse calculations
• Find the surface area and volumes of the cone and
  sphere to include inverse calculations.
• Find the surface areas and volumes of compound
  shapes most of which are everyday objects.
• Distinguish between formulae for perimeter, area
  and volume by considering dimensions.

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