LESSON 9.1
Areas of Rectangles and Parallelograms
AREA OF A RECTANGLE
C-81: The area of a
rectangle is given
by the formula
A=bh. Where b is
the length of the
base and h is the
height.
AREA OF A
PARALLELOGRAM
C-82: The area of a
parallelogram is
given by the
formula A=bh.
Where b is the
length of the base
and h is the height
of the
parallelogram.
LESSON 9.2
Areas of Triangles, Trapezoids and Kites
AREA OF TRIANGLES
C-83: The area of a
triangle is given by
the formula bh .
A 
2
Where b is the
length of the base
and h is the height
(altitude) of the
triangle.
AREA OF TRAPEZOIDS
C-84: The area of a
trapezoid is given
by the formula
(b  b )h
A 
. Where the b's2 are
the length of the
bases and h is the
height of the
trapezoid.
1
2
AREA OF KITES
C-85: The area of a
kite is given by the
d gd
formula A 
.
2
Where the d's are
the length of the
diagonals of the
triangle.
1
2
LESSON 9.4
Areas of Regular Polygons
AREA OF REG. POLYGONS
A regular n-gon has "n"
sides and "n" congruent
triangles in its interior.
The formula for area of a
regular polygon is derived
from theses interior
congruent triangles.
If you know the area of
these triangles will you
know the area of the
polygon?
FORMULA TO FIND AREA
OF A REGULAR POLYGON
n= # of sides
a = apothem
length
s = sides length
bh
A  ng
2
as
A  ng
2
na s
A 
2
FORMULA TO FIND AREA
OF A REGULAR POLYGON
C-86: The area of a regular polygon is given by
the formula
nas, where a is the apothem
A 
(height of interior triangle),
s is the length of each
2
side,
and n is the number of sides the polygon has.
Because the length of each side times the number
of
aP
A
P  sn
sides is the perimeter, we can say
and 2
.
LESSON 9.5
Areas of Circles
AREA OF A CIRCLE
C-87: The area of a
circle is given by
the formula
,
Ar 
where A is the area
and r is the radius
of the circle.
2
LESSON 9.6
Area of Pieces of Circles
SECTOR OF A CIRCLE
A sector of a circle is
the region between
two radii of a circle
and the included arc.
Formula:
C entral A ngle
360

A rea of Sector
r
2

AREA OF SECTOR
EXAMPLE
Find area of sector.
C entral A ngle
A rea of Sector

360
45
x

360
12
1
x
9
144

r
2
144
 x
9
16  x

2

SEGMENT OF A CIRCLE
A segment of a circle
is the region
between a chord of a
circle and the
included arc.
Formula:
A rea of Segm ent=A rea of Sector - A rea of T riangle
See E xam ple on N ext Slide
SEGMENT OF A CIRCLE
EXAMPLE
Find the area of the
segment.
90   6 g6 
 2
 6  g360    2 

 

 36 
1

36
4

36
2
  18
4
 9   18 cm
2
ANNULUS
An annulus is the
region between two
concentric circles.
Formula:
A  R  r 
2
2
LESSON 9.7
Surface Area
TOTAL SURFACE AREA
(TSA)
The surface area of
a solid is the sum of
the areas of all the
faces or surfaces
that enclose the
solid.
The faces include
the solid's top and
bottom (bases) and
its remaining
surfaces (lateral
surfaces or
TSA OF A RECTANGULAR
PRISM
Find the area of the
rectangular prism.
TSA  2 ( 4 g10 )  2 ( 7 g4 )  2 ( 7 g10 )
 80  56  140
 276 cm
2
TSA OF A CYLINDER
Formula:
TSA  2(r  )  2 r  gh
2
Example:
TSA  2 (6  )  2 (6 ) g20
2
 2 ( 36  )  240 
 72   240 
 312  un
2
TSA OF A PYRAMID
The height of each
triangular face is
called the slant height.
The slant height is
usually represented
by "l" (lowercase L).
Exampl
e:
TSA  B ase A rea  Lateral Surface A rea
 32 g25 
 25 g25  4 

 2 
 625  4 ( 400 )
 625  1600
 2225 ft
2
TSA OF A CONE
Formula:
•
TSA  Area of Base  Lateral Surface Area
 r   r l
2
•
Example:
TSA  8   8  9
2
 64   72 
 136  cm
2